dw B) Use the chain rule to find the derivative dt of w = x2 + y2 with x cost, y = sint.

Q: Find the directional derivative of z = f (x, y) = x²y³ – 3y² at (-3,4) in the direction of the…

A: Use directional derivative formula which is mentioned in solution.

Q: Compute the indicated derivative using the chain rule. dy x = 4 + 3t, y = -7t; dx dy dx ||

A:

Q: Find the derivative of the function f (x, y) = x²y + y²z: at Po(1,2,3) in the direction of û = 2î –…

A: To find the derivative of the function f(x,y)=x2y+y2z at P0(1,2,3) in the direction of…

Q: Compute the indicated derivative using the chain rule. x = 6 + 3t, y = −8t;  dy dx

A:

Q: Find the derivative of y with respect to t. 10t y3Dcsc dy %3D dt

A:

Q: Compute the indicated derivative using the chain rule. dy x = 1 – t/3, y = 8t – 1; dy %3D

A:

Q: Find partial derivative of dx for the function f(x,y) given below exp 2x. siny .(at the point (In2,…

A:

Q: Use the chain rule to find the derivative of w= x + y with dw with x cost + sint, y= cost– sint dt…

A:

Q: Find the derivative of y with respect to t. y= sin 1(10t) dy dt %3D

A:

Q: Find the derivative of y with respect to x. y = In (x) dy 8. dx %3D

A:

Q: Find the partial derivative of the given In[y? sec(x²y²)].

A:

Q: Compute the indicated derivative using the chain rule. dy x = 5 + 3t, y = -8t; dx dy %3D dx

A: We have to find the indicated derivative by using chain rule: x=5+3t, y=-8t Differentiating first…

Q: Find the derivative d dy dy (3y?) = ay + by +c- dt dt dt

A: Proceed as shown below....

Q: Find the derivative of y with respect to 1. y = In V4x2 + 7x %3D 2. y = sec?(e-4*)

A: A detailed solution is given below.

Q: Find the derivative of y = 7 In(sin t + 5). dy/dt =

A:

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: Find partial derivative of dx for the function f(x.y) given below exp 2x. siny .(at the point (In2,…

A:

Q: Find the derivative of ƒ(x, y) = xey + cos (xy) at the point (2, 0) in the direction of v = 3i - 4j.

A: Given: f(x,y)=xey+cos(xy) at point (2,0) in the diection of v=3i−4j

Q: Compute the indicated derivative using the chain rule. X = 4 + 3t, y = -7t; Oy

A:

Q: Find the derivative of the function. s=t° In t| ds dt

A: The solution is given below in the next step:

Q: Find the derivative of y with respect to x. y= sec -1(3x? + 1), x>0 dy dx

A: Given that: y=sec-1(3x2+1), x>0

Q: Find the derivative of the function. -1 y = (3t – 1)(6t – 5) dy dt II

A:

Q: Find the derivative of this complex function: where z=x+jy (2+jj?

A:

Q: If we are getting the partial derivative of f(x,y) with respect to x, we are letting the y variable…

A: hello greetings from bartelby.i am here to help you.

Q: What is the derivative of y = sin1 (x² + 2)? dy dr /1-(z²+2)² dy O dr 2x V1-(2²+2)² O dz V1+(x²+2)²…

A:

Q: dy By using the "definition of the derivative" find of y = V2x? dx

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: What is the derivative of y = tan-1(x2 + 1)? dy dr 2 1+( z²+1)² dy dr /1+(z²+1)² dy O dr V1+(2+1 )°…

A: To find derivative of y=tan-1x2+1

Q: Compute the indicated derivative using the chain rule. dy x = 1 - t/3, y = 8t – 1;- dx dy dx

A: x=1-t3 differentiating with respective t dxdt=-13 y=8t-1 differentiating with respective t dydt=8

Q: Find the first-order partial derivative with respect to x of f(x,y) = e5x siny.

A: To find the first-order partial derivative with respect to x, given function, fx,y=e5x sin y

Q: B: Use the Chain Rule to find the derivative of f(x,y) xy with respect to (t) along the path y =…

A: Solution:-

Q: Find dw/ds and dw/dt using the appropriate Chain Rule. Function Values w = sin(4x + 5y) x-s+t, y =…

A: The given function,w=sin(4x+5y)x=s+ty=s-tat the point s=0, t=π2

Q: Find the derivative of y=cos^3w+cos(w^3) dy/dw=

A:

Q: Use the Chain Rule to find the derivative of w = xy with respect to t along the path x = cos t, y =…

A:

Q: Find the indicated derivative. dy dt - for y = (2.2t - 4t?)(2t + 1.9) dt 11

A: We have to find dy/dt for Given function.

Q: Find the derivative of F(x)

A: To Determine: find the derivative of F(x) Given: we have Fx=∫2x3costdt Explanation: we have a…

Q: Find the derivative of y with respect to z. y=3 (2°) dy dz II

A: We have to find the derivative of y with respect to z when y=3z9 Taking log both sides,…

Q: dy Find by using Chain Rule for y = sin³4t dt

A: Here we do u and v subsitution to get the derivative of given function.

Q: dy Differentiate implicitly to find xp ex*y = 7x+ 3y +3 Evaluate the derivative of the each side of…

A:

Q: If z = (x + y) e and x = 3t and y = 1 – t, find the following derivative using the chain rule. Enter…

A:

Q: B: Use the Chain Rule to find the derivative of f(x,y) = xy with respect to (t) along the path y =…

A:

Q: dy Compute the derivative y' dt 2t – 9 - y = 5t 2

A:

Q: Find the derivative of the function. y = (3t – 1)(6t – 6) -1 dy dt II

A:

Q: Compute the derivative y = dy %3D dt 2t - 7 y = 7t- 3

A:

Q: Compute the second derivative of e^x+y+y^2+x^3=0. y" denotes, d^2y/dx^2

A:

Q: Find the partial derivative. z = sin (9x'y – 10æy?) dz

A:

Q: Use the chain rule to find the derivative of the function z = 2a*y³ – xy? along the curve given by x…

A:

Q: The second derivative d^2y/dx^2 of y^3 = xy + 1 at the point (0,1) is

A: