1. Find the directional derivative of the function f(x,y) = 2x²y + 6xy at (1, 1) in thedirection of a unit vector whose angle with positive x-axis is

Answered: Image /qna-images/answer/8a4cb1bb-c4b3-4848-962c-45f30a157f6b.jpg

Answered: Find the directional derivative of the…

Find the directional derivative of the function f(x, y) = 2x2y + 6xy at (1, 1) in the direction of a unit vector whose angle with positive x-axis is

Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Topics In Analytic Geometry

Section6.2: Introduction To Conics: parabolas

Problem 4ECP: Find an equation of the tangent line to the parabola y=3x2 at the point 1,3.

See similar textbooks

Related questions

Q: 1. f(x, y) = 1+ 2x/y, (3,4), v= 4î – 3ĵ |

A: According to our company policy we can answer only first question and rest can be reposted. Thanks

Q: (a) Find the directional derivative of f (x,y) = In(xy) at (-) in the direction of (1,1).

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find the directional derivative of the function f: R2→R, f (x, y)= xy2 + x2y in the direction of…

Q: Find the directional derivative of f(x, y, z) = -4x? + ly? – 4z2 at the point (0, -4, 2) in the…

A: Given function

Q: Find the directional derivative of the function at the given point in the direction of vector v.…

A: The objective of the question is evaluate the directional derivative at the given point and…

Q: Find the directional derivative of the function f(, y) = In(x + y°) at the point (- 1,3) in th…

Q: What is the gradient of a function f(x, y) and why might we want to calculate it? How does it relate…

A: Properties of gradient of function

Q: Compute the directional derivative of the function g(x,y) = sin (x(4x – 5y)) at the point P(3, – 3)…

Q: find the directional derivative of f(x,y,z)=3e^xcos(yz) at P(0,0,0) in the direction of A=2i+j-2k

A: First find out the partial differentiation of f(x,y,z) and then put the values (0,0,0) and then for…

Q: Find the directional derivative of f(x,y,z)=z^3−x^2y at the point (-1, 1, -4) in the direction of…

Q: Find the directional derivative of the function f(x, y) = 1+5x/ỹ at the point (5, 1) in the…

Q: Find the directional derivative of f(x, y, z) = z3 – x²y at the point (5, -2, -2) in the direction…

Q: Find the directional derivative of the function f (x, Y, z) = 6x² –- 2xy + yz in the direction of…

Q: Find the directional derivative of f(x, y, z) = zy + xª at the point (2, 1, 3) in the direction of a…

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…

Q: In what direction ữ is f(x, y, z) increasing most rapidly at the point (1, 1, 0)? Give your answer…

Q: Find the directions in which the directional derivative of f (x, y) = ye*y at the point (0,2) has…

Q: : Find the derivative of the function at Po in the direction of the vector AC. f(x, y, z) = x² + 2y²…

A: To find the directional derivative of the given function.

Q: Let f(x, y, z) = xy² 23 Find the directional derivative of the function at the point (1,-2,1) in the…

Q: Find a vector equation of the tangent line of f(t) = (cost, sint, t) at the point Po (0, 1,

Q: Find the directional derivative of the function at the given point in the direction of the vector v.…

A: Givenf(x,y)=xx2+y2 , (2,1) , v=<3,5>

Q: Find the directional derivative of the function f(x,y, z) = V22+ y² + z² at point (2, -3, 6) in the…

A: In this question, we want to find the directional derivative of the given function at given point…

Q: Find the directional derivative of f at the point (1,2) in the direction of the vector v = = (1, 3).

Q: Find the directional derivative of the function z(x, y) = In(x² + y²) at the point M(xo, Yo), in the…

A: The directional derivative of function z=fx,y in the direction vector u is calculated by the formula…

Q: Determine the directional derivative of the following functions in the vector direction specified at…

A: Here we will find out the required value.

Q: Compute for the directional derivative of f (x,y,z) = tan (ax – 2ny)e4y-z at the point (,0, ln 4) in…

Q: Find the directional derivative of f(x,y) = x² + y² – 2x – 4y at the point (-2,3) in the direction…

Q: Find the directional derivative of f(x,y,z)=yz+x^4 at the point (1,2,3) in the direction of a vector…

A: According to the given information, it is required to find the directional derivative.

Q: Find the directional derivative of the function f(, y) = In(x +y°) at the point (- 1,3) in the…

A: As per our guideline we are allowed to do 1 question at a time. Please post other questions next…

Q: Find the directional derivative of function f(x y)=x°e' at the point (1,1) and direction of vector…

A: Given: fx,y=x2ey at the point 1,1 and direction of vector v=2i fxx,y=∂∂xx2ey…

Q: Find the directional derivative of the function at the given point in the direction of the vector v:…

A: Since solve the first question for you. If youwant any specific question to be solved then please…

Q: find the derivative of f(x, y) = x² + xy at P,(1,2) in the direction of the unit vector u = i+ V2

Q: b. Find the directional derivative of the function z = x3 – y3 at the point M(1,1), in the direction…

Q: find the directional derivative of the function in the direction of the vector u = cos i + sin j

A: Consider the given function, fx,y=sin2x+y Here we need to find the directional derivative of the…

Q: Find the directional derivative of the function at the given point in the direction of the vector v.…

A: Here we use the formula, Dvf(x,y)=∇f(x,y).v

Q: Find the directional derivative of f(x, y, z) = x²y−yz³ + z at the point (1,−2, 0) in the direction…

A: Solution:f(x, y, z) = x²y−yz³ + zat the point (1,−2, 0) in the direction of the vector a = 2i +…

Q: Find the directional derivative of f(x, y) = 10 − 3x^2 + (y^4)/4 at P(2, −3) in the direction of the…

Q: Find the directional derivative of the function f(x, y,z) =x-y+2z at the point P(1,2,3) in the…

A: Note:- Let a function f(x, y, z), then Direction Derivative of the function f at point P in…

Q: Find the directional derivative of the function f(x, y, z) = /ryz at the point P(2,2, 2) in the…

A: Topic-vector calculas

Q: Find the directional derivative of the function f = In (x² + y2) at the point P(4,5) in the…

A: By Bartleby policy I have to solve only first one as Q)3)a) and Q)3)b) are unrelated problems.These…

Q: Find the directional derivative of f(x, y, z) = x²y²z + 4xz at (-1,2,1) in the direction 2i + j +…

A: We have to find the directional derivative of f(x, y, z)=x2y2z+4xz at (-1, 2, 1) in the direction…

Q: The directional derivative of f(x, y, z) = xyz at point (-1, 1, 3) in the direction of vector î - 2ĵ…

A: Remark: We know that the directional gives the rate of change of a function at a specific point in…

Q: Find the directional derivative of the function f(x, y) = 1+5x/ at the point (5, 1) in the direction…

Q: Find the directional derivative of the function f(z, y) = In(z° + y*) at the point (3, – 1) in the…

A: We can solve this as follows:

Q: Compute the directional derivative of the function f(x,y) = - xy + y at the point P(0, - 9) in the…

A: Solution-

Q: Find the directional derivative of f (x, y, z) = xy²z³ at P(2,1,1) in the direction of Q(0,–3,5)

A: Solution: The objective is to find the directional derivative of the given function

Q: Find the directional derivative of function f(x,y)=x*e" at the point (1,1) and direction of vector…

Q: Find the directional derivative of the function f(r, y) = 1+5x/j at the point (5, 1) in the…

Q: Find the directional derivative of the function f(x, y) = x²y° in the direction of the vector at…

A: Concept:

Q: What is the directional derivative of f(x, y) = 4xy+ y cos x at the point (0, 1) in the direction of…

Q: Find the directional derivative of the function at the given point in the direction of vector v.…

Question

1. Find the directional derivative of the function f(x,y) = 2x²y + 6xy at (1, 1) in the
direction of a unit vector whose angle with positive x-axis is

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Differentiation$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

Similar questions

Find an equation of the tangent line to the parabola y=3x2 at the point 1,3.
Consider the function defined by f(x,y) = 4xy - 2x2. Evaluate the directional derivative of f at point(1,-1) in direction of the vector which subtends an angle of pi/6 with the positive x-axis.
Find the directional derivative of g(a, b) = cos(3a + 4b) at the π point ( along the direction of the vector (-4,-3)
b. Find the directional derivative of the function z = x3 – y3 at the point M(1,1), in the direction of the vector u which makes angle a = 60° with positive direction of the x- axis.
2. Find the directional derivative of 9 = yx? +x?z + 3xyz in the direction of vector n = Î + 2ŷ -? .
Find the directional derivative of the function at the given point in the direction of the vector v. f(x, y) = 7ex sin(y), (0, ?/3), v = (-3,4)
Compute the directional derivative of the function g(x,y) = sin((5x - 4y)) at the point P(3,3) in the direction vector. The directional derivative is (Type an exact answer, using as needed.) C Be sure to use a unit vector for the direction
Find the directional derivative, Dчf, of the function at the given point in the direction of vector v. f(x, y) =2ln(x²+y²), (2, 3), v = Duf(2, 3) =
Compute the directional derivative of g(x,y)=sin(pi(5x-5y)) at point P(1,-3) in the direction (15/17, 8/17). Be sure to use a unit vector for the direction vector.
Consider the function f (x, y) = 5x² - 6y². Find the directional derivative of f at the point (−1, −4) in the direction given by the angle = (Here is the polar angle -- the angle which the direction makes with the positive direction of the x-axis.) Find the unit vector in the direction in which f is increasing most rapidly at (-1,-4).
Find the directional derivative of the function at the given point in the direction of the vector v.
(a) Find the directional derivative of z = x²y at (5,5) in the direction of π/2 with the positive x-axis. (b) In which direction is the directional derivative the largest at the point (5, 5)? Enter your answer as a vector whose length is the largest value of the directional derivative.