Use the chain rule to find the derivative of 15 f(x) = 4( – 5æ5 You do not need to expand out your answer. f'(x) :

Q: Find the derivative of y = 6e x – cosx.

A: Given function, y=6ex-cosx Used formulas, ddxcfx=cddxfx  c=constantddxex=exddxcosx=-sinx

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: Find the second derivative for the functions defined as follows.h(x) = x/ex

A: Given:             f(x)=xex

Q: Find the derivative of the function.

A: Given function is By using the properties of logarithm, ln(a/b)=ln(a)-ln(b) and ln(a^b)=bln(a), we…

Q: Use the Chain Rule to find the derivative. y = sin(x2)

A:

Q: Find the derivative of the function. y = In(t2) – arctan 3 y' =

A: It is derivative.

Q: B. By using the definition of the derivative, find the for: - dx f(x) = x -

A: Explanation of the answer is as follows

Q: Find the derivative of the function. 5x g(x) = [¨ cos(r}]dt cosx

A: We will use Lebnitz rule to differentiate the function .

Q: Use the chain rule to find the derivative of the function z = x2y3 − x along the curve given by x =…

A:

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: Use the General Power Rule, Exponential Rule, or the Chain Rule to compute the derivative. y = cos…

A: Given that y=cos6θ+15 Find dydθ Needed formulae: xn'=nxn-1 cos x'=-sin x ax'=a

Q: What is the derivative of y = cos-1 (x² + 2)? %3D

A: Derivatives formula ddxcos-1x=-11-x2 ddxxn=n xn-1

Q: Compute the derivative using derivative rules.

A: Explanation Given that,  y=(kx+b)-13   Differentiate with respect to x both the sides…

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

A:

Q: Find the derivative of f(x) = ln∣cos x∣.

A:

Q: Use the Chain Rule to find the derivative. y = sin2 x

A: Given the function fgx. The derivative of the expression using chain rule is f'gxg'x. The derivative…

Q: What is the derivative of y = ekx? For what values of k does this rule apply?

A: Given function is, y=ekx. The derivative of the given function is found as follows: dydx=ddxekx=kekx

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

A: We have given y=cos3e4θ Then, dydθ=dcos3e4θdθ=3cos2e4θ-sine4θ4e4θ=-12e4θsine4θcos2e4θ

Q: Find the derivative of the function. 1 3x' g(x) = dt 1 + t4 Jtan x

A: Given : g(x) = ∫tanx3x211+t4dt

Q: Compute the derivative of the function y=x2/ln x at x=e.

A:

Q: Find the derivative of the function. y = 2 cos5 x

A: Given, y = 2 cos5 x To evaluate, dydx

Q: Find the derivative of f(x) = x² cos r.

A: The given function fx=x2cosx Differentiate with respect to x using the product rule…

Q: use the Chain Rule to find the derivative. y = sin2 x

A: To differentiate: y=sin2x Solution: y=sin2xDifferentiating both sides w.r.t x we…

Q: 1. x + y + xy = 21

A: We will use simple differentiation rules to solve this question.

Q: Compute the derivative using derivative rules. y= cos(1/x) / (1 +x 2)

A: Derivative: The rate of change of a function with respect to a variable. y=fxy'=limh→∞ f(x+h)-f(x)h

Q: Find the derivative of the function y = 2x arccos x − 2√(1 − x2 )

A: If the two functions f(x) and g(x) are differentiable (the derivative exist) then the product is…

Q: Use the chain rule to find the derivative of 2e9z7 Use e^x for e".

A:

Q: Find the derivative of f(x) = -1 csc (cos r)

A:

Q: Find the derivative of the function. h(x) = x² arctan(8x) %3D

A: To find the derivative of hx=x2tan-18x

Q: Find the derivative of the function.

A: Given: y=ln(x4)(1,0)

Q: Use the Chain Rule combined with other differentiation rules to find the derivative of the following…

A: Given: y=xx+15 To Find: The derivative of the given function

Q: Find the derivative of the function using the Power Rule for Functions. y = (x² + 6)²(4x³ – 1)3 dy…

A: Y'= ?

Q: Use the chain rule and product rule to find the derivative of f (x) = e" (sin(x)² + x).

A: Given Data: Function: ex(sin(x)2+x)   The chain rule of the derivative is, ddxfgx=fgxg'x ......1…

Q: Find the derivative of the function y = 2x − cosh √x

A: The given function is y=2x-cosh x. Obtain the derivative of y=2x-cosh x as follows.

Q: (a) h(x) = tan(r'sinx

A:

Q: y = cof'/ x2-1 x²+

A:

Q: Find the derivative of y = x 1 cOS x 2

A:

Q: Find the derivative of the following using the three-step rule 2. y=Va² +x

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Q: 5. f(x)%3D + cos X

A:

Q: find the 2nd derivative of the function defined implicity by the equation x^1/3+y^1/3=80

A:

Q: e derivative of y with respect to x. y= 2sin^-1(5x^4

A: we have to find the derivative of y with respect to x.y=2sin-1(5x4)

Q: Find the 10th derivative of y = cos 3x. f(10)(x) =

A: Given, y=cos3x

Q: Use the Chain Rule to find the derivative.

A: First of all, consider the formula for the chain rule and the given function y. Then assume u and v…

Q: Find the derivative of f(x) = ln v4 – x2 %3D

A:

Q: What is the derivative of the function B(x)=3/(x+2) at x=a?

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Q: Find the derivative of f (x) =arcoth (e³" ).

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Q: c. Find the derivative of y =+- et x3 cOS X 2

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Q: r(x)= cos (3x)

A: