Use the chain rule to find the derivative of the function z = x2y3 − x along the curve given by x = cos θ, y = sin 2θ. Give your answer in terms of θ.

Q: Find the derivative of the function 1-x2 t2sin(t) dt g'(x) =

A: First I have written the Leibnitz rule for derivative of an integral and using them find the…

Q: Find derivative of the following function. 5x -5x y%3D dy

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Q: Use the Chain Rule to find the derivative. y = sec 1/X

A: Differentiate: y=sec 1x. Apply chain rule: dydx=dydu·dudx Let u=1x dydx=dsec 1xd1x·d1xdx

Q: Calculate the derivative of the function xe" at the point x = 0 %3D O 1 e O 2e

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Q: Find the derivative of the function. y = cos(aª + x*) y'(x) =

A: f(x)  =  cos x4 + a4ddx f(x) = f'(x) =…

Q: Find the derivative of the function y=ax+ba+b, where a and b are constants.

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Q: Find the derivative of the function.

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Q: use the Chain Rule to find the derivative. y = cos3(e4θ )

A: Given: The function given is  y=cos3(e4θ)   To determine: The derivative of the function y=cos3(e4θ)…

Q: Find the derivative of z=tan(e^-7w) dz/dw

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Q: Use the Chain Rule to find the derivative of the following functions.

A: To find the derivative of y=1-ex4 using the chain rule. Solution: Chain rule of differentiation…

Q: Find the requested higher-order derivative for the given function. d3y of y = x" - sec(x) dx3

A: Given that y=x11-secx and we have to find third order derivative of y with respect to 'x' that is…

Q: Use the Power Rule to compute the derivative: d. X. dx x=-1

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Q: Find the third derivative. 1 (x + y)Z + (x – y)Z = a

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Q: Find the 30th derivative of y = cos(2x). f(30)(x) =

A: Take the derivative multi times and observe the pattern then write the required answer.

Q: Find the derivatives of the functions in Exercise . y = (1 + x2) e^tan-1 x

A: Given,          y=(1+x2) etan-1x

Q: Find the derivative of y with respect to x if y = (13x - 26x+26) e -8x y =D %3D

A: Explanation of the answer is as follows

Q: Find the derivative. y = In(t5t)

A: Consider the given equation y=lnt5t and simplify it. Use the logarithmic properties to simplify it.…

Q: compute the derivative. g(t) = sinh(t2)

A: g(t)=sinh(t2)

Q: Find the derivative of the function. F(t) = est sin(2t)

A: Use the chain rule of derivative and simplify.

Q: Find the derivative of the function. = cos (a° + a") y = cos

A: Given,            y = cosa9 + x9

Q: Use the Fundamental Theorem of Calculus to find the derivative of y- " cos t dt t12

A: Given that  y=∫-9xcos tt12dt

Q: Z = 1+x2 ; d'z/dx?

A: Given: Z = 21+x2 To find: The derivative, d2 Zdx2 in simplified form.

Q: Find the derivative. y = In /x+7 y' = D

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Q: Find the derivative of y with respect to t. y= sin(6t)

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Q: Find the derivative of the function R = sin(7t

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Q: Find the derivative. F(t) = In(sinh(2t)) %3D F'(t) %3D

A: Find the derivative of the function

Q: Use the rules of differentiation to find the derivative of the function.

A: We know that, from the rule of differentiation ddxk·fx=k·ddxfx            ⋯⋯1 where k is any of…

Q: Find the derivatives of the function defined as follows.

A: Consider the given function y=cos xcos 4x   Apply the chain rule: ddxy=ddxcos xcos 4xy'=12cos xcos…

Q: Compute the derivatives. Use the fact that e2+x = e2 . ex to find d/dx (ex+2).

A: ddxex+2

Q: Find the derivative of y with respect to x, t, or 0, as appropriate. y 2xe X- 2e X O 2xeX O 2xeX +…

A: Finding the derivative

Q: Let f(x,y) = x³y? The third derivative fexy

A: NOTE: Refresh your page if you can't see any equations. . take the partial derivative with respect…

Q: Find the derivatives of the function defined as follows.

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Q: Cos 0 d0 y =

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Q: Find the second derivative of 1. F(x) = tan(2x) 2. F(t) = e^t sint

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Q: Find the derivative of the function. 9x g(x) = [™ cos(r³]ct Cosx

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Q: The derivative of the function y = tan(In(vx² – 6x + 1)) is: %3D

A: Formula:ddx(tan x) = sec2xddx(ln x) =1xddx(xn) =n xn-1

Q: Find the given flx), + 2x derivative of function. %3D a+x

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Q: Find the derivative of the function. F(t) = 5t sin(mt)

A: To find the derivative of the given function f(t) we use product rule for derivative, Since f(t) is…

Q: Find the derivative of the function. y = a° + cos (x) y'(x)

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Q: The 2nd derivative of the function x = Ci cosot + C2 sin ot with respect to t is

A: Given function is

Q: Use the Quotient Rule to find the derivative of the function.                                f(t) =…

A: the quotient rule of the derivative states dydt=v.dudt-u.dvdtv2 here v=t3,u=cost we will derivate it…

Q: compute the derivative g(t) = sinh(t2)

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Q: f(t) = sin²(e in²s) %3D

A: Given : ft = sin2esin2t

Q: Can you help me step by step?

A: Assume p=x^2*sin^9 xThen find derivative of p w.r.t. xUse product rule and chain rule for this.

Q: a) f sin(x) cos(x) dx,

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Q: Use the Chain Rule to find the derivative. y = tan(θ + cos θ)

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Q: The derivative of the function () y = In is: tan x,

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Q: Compute the derivative of the given function. f (x) 10x-1/4 cos e + 7 sin a %3D -

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

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Q: Find the derivative of the function. y = sin ( r2 + 1 )

A: Our Aim is to find the derivative of the function given below:-y=sin (r2+1) -(i)