Problem 4. Consider the function f : R² →R given by f(r, y) = y² – 2r². Find the directional derivative of this function at the point (1,1) in the direction (2, 1)".

Q: Question 1 Consider the curve defined by 2y3 + 6x2y - 12x² + 6y = 1. dy 4х - 2ху (a) Show that dx x2…

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Q: QUESTION 12 dy Find by implicit differentiation. de e -x6+y6 =-5 a. 6y- yey xe + 6x b. 6x -xey ye +…

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Q: What is the equation of the line tangent to the curve e" + cos(x) = 1 at the point C.0. y =1- ... A…

A: Given; ey+cosx=1 at point (π/2,0).

Q: Find an equation of the tangent line at the given point on the curve. (a) x = 2 – 3 cos 0, y = 3+ 2…

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Q: Find an equation of the tangent line at x= a. x- y%3D a = 2 4 10 A. y=x+1 *B y=x-1 y3x-1 Xe y=x+2…

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Q: 4. Find the equation of the tangent line to f = 10** at x = 0. А. у %3D 1 B. x = 1 D. y = x – 1 E. y…

A: Tangent line equation =>y – y1 = m (x – x1), where m is the slope and (x1, y1) is the coordinate…

Q: 7) What is the equation of the tangent line of f(x) = xe"+ 3, at x = 0 a) Y= x+3 b) Y= 3 c) Y=…

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Q: Suppose u and y are functions of x that are differentiable atx = 0 and that u(0) = 5, u(0) = -3,…

A: To Determine: find the values of the following derivatives at x=0                a)ddx(uv), b) ddxuv…

Q: Find the directions in which the function f(x,y) = x²y + e* sin(y) Increase and decrease most…

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Q: 1- find dy/dx as a function of x. y = sec (tan x) 2- find dy/dx etty = 2x + 2y %3D 3- find an…

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Q: If f(x,y) = ln(xy) + x2y2, in what directions is the second directional derivative of f(1,1) = 3?

A: Given function fx,y=lnxy+x2y2 Consider unit vector u⏞=12,32  Now, Du⏞f=∇f·u⏞             ∇f=fx,fy…

Q: x +1 at (2,3) is x- 1 The equation of the tangent to the curve g(x) = 1) y = -2 2) y = 3x - 3 3) 2x…

A: To find the tangent to the curve

Q: I need help with 1a)

A: straight line becomes y=x

Q: 15. Find the equation of the tangent line to the curve at point (0, In 2). y = In(e' + e4) O 2y + 5x…

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Q: 19. The slope of the tangent to the curve (x2 + y²)² = 4.x²y at the point (1, 1) is 3 3 (a) - () – 1…

A: We have to find slope of the tangent to the curve x2+y22=4x2y at the point 1, 1. We know slope of…

Q: (d) Suppose that y(x) is a function and that y(2) = 1. Let y² + y = x. Using implicit differentian…

A: y2+y=x  Differentiating both sides with respect to x  ddxy2+y=ddxx    2y+1y'=1    y'=12y+1

Q: Problem 9. Find the derivative of the function at the point Po in the directic of the vector u: a)…

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

Q: Find the equation of a line normal to the curve of y= cos at x= 1. Select one: A. -33 x + 9y - 9 +…

A: Equation of Normal

Q: Q. No. 5. Find the Derivative of the Given fur a) y= ev1n x( Inx) +2x b) f(x) = %3D a+x

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Q: Find the differential dy. y = (x+4)/(x-4)

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Q: 30. Find an equation for the tangent plane to z = f(x, y) at (3, -2) if the differential at (3, -2)…

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Q: 10x Find the directional derivative of f(x,y) = at P(5,0) in the x + y direction of Q(4, –3). NOTE:…

A: Here is the solution:

Q: If a curve f(x) has dx dy = (y – 1)2(2+ x) and passes through the point (-1,2), then what is the…

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Q: 6. Find where the velocity of a particle is zero if its position function is x(t)= t In t

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Q: Question 10 Find the partial derivative of z with respect to x (8) f ах (22−y) = Əz C dz 2(x-y) 2²…

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Q: Problem 1 Consider the function: S(z, v) = sin(2z + 3y). (a) Find the gradient of f. 2. (b) Evaluate…

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Q: QUESTION 3 Determine the directional derivative of xy + xZ + yz at (1,2, - 1) in the direction of 2i…

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Q: 1. Find the first derivative of y with respect to x (y') of the given functi 1. x³y-xy² +x² +y? = 0…

A: To find the first derivative of y using the given equation.

Q: Find the equation of the line tangent to y 8xe" at x = 1. O y -8e = 16e(x – 1) O y - 8e = 8e(x – 1)…

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Q: 1) Find the Linearization x of the function -V1+2x when x is near 0 Find the equation of the tangent…

A: As per Bartleby guideline if more than one question is asked only first question to be answered…

Q: 13. Find the derivative of the function T(z) = dz +b cz +d numbers such that ad – bc + 0. When is…

A: Hello. Since your question has multiple parts, we will solve first question that means question (13)…

Q: d 1) Find sec dt t2 - 3t 2) Find the derivative of y t+1.

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Q: Question 8 Let f (x, y, z) : = xz cos(y). Find the directional derivative of f at (1,0, 2) in the…

A: Solution

Q: 1. (a) Find an equation of the tangent plane to the graph of x² + y² + z² = 16 at (0, 2, 2√3).

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Q: Q1: a) Find the directional derivative of S = In(2r +3y) at point (-1,1) in the direction of 4i -3i…

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Q: Question 3 Consider the function f(r, y) = 2x + 4y² %3D and the curve y(t) = (sin t, cos t), te…

A: Introduction: For a given function fx,y and a curve rt=xt,yt, their composition is frt=fxt,yt. The…

Q: 2. Find the first and second derivatives of the following functions a) y = 6) y = e", c) y = In (sin…

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Q: 1. If an object moves with velocity v(t) = sin(t) + 3t and begins at position p(0) = 0, find the…

A: integration of velocity funct

Q: 1. Consider the curve F(x, y) = 0. Show that if F has continuous second derivatives, then a formula…

A: Consider the curve F(x, y)=0. The objective is to show that if F has continuous second derivatives,…

Q: Question 5 Consider the function f(x, y, z) = x cos(xy² z). Compute the value of the derivative fr…

A: Solution

Q: 2. If g(x) = x + 2 cos x, then the equation of the tangent line to the graph of g at x = is A. 2y +…

A: Equation of tangent line through A(x1 , y1) is given by :- y – y1 = slope x (x – x1)

Q: Question No. o3 Calculate the directional derivative the of 2. function $ (*,y, 5) = xy+ ya* at te…

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Q: Let zy Find dx dt dy dt 3 and when I 2. 2.

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Q: Find the derivative of the following functions/parametric equations. 4. e2x cos y + y2 = 1

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Q: 3. Find the equation of the tangent line to the curve at (1,2) * y = 5 - x O A. x-6y + 22 = 0 O B.…

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Q: 7) Let x = t – sin(t) , y = 1– cos(t). Determine the equation of the line tangent at t = n.

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