The function g is related to a parent function f(x) = cos(x).

Q: Find the derivatives of the following functions. g(x) = x² cos(x).

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

Q: Find the derivative of the function g(x) = 3arccos(x/2)

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Q: 3. Find the derivative of the following functions: a. f(x) = (x² + 1)(x³ – 2x² – 1) f(x) = b. 2 +…

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Q: Evaluate the derivatives of the following functions

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Q: f (x) e1/x x2

A: Given function is fx=e1xx2

Q: Find the first and second derivatives of the function. g(t) = 2 cos t - 3sin t

A: We find the first derivative

Q: Find a formula for df 1 dx for the function below using the Derivative Rule for Inverses. f(x) = (5…

A: Given,         fx=5-3x3We know that,           The Derivative Rule for inverses is given by…

Q: Evaluate the derivatives of the following functions.

A: ddxarcsin(esin(x)=11-(esinx)2·ddxesinx=esinx·ddxsinx1-e2sin(x)=esinxcos(x)1-e2sin(x)

Q: The graph of the derivative f' of a function f over the interval (0, 16) is shown. y y =f '(x) 10 12…

A: Given that: Graph of f'(x)     NOTE: As per our answering guidelines, we can only answer 1 question…

Q: Find the derivative of the function. 8. g(t) = t2 CO |回

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Q: Find the first and second derivatives of the function  G(t) = 2 cos t - 3 sin t

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Q: Use the chain rule to compute the derivatives. a) f(x) = sin? x = (sin x)? b) f(x) = sin(x²) c) f(x)…

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Q: Find the first and second derivatives of the following function: g(t) = t°et gʻ(t) g"(t) = %3D

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Q: 1. Calculate the derivatives of the following functions. a) f(x) = In (In(x)) 4x3 b) g(x) =…

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Q: Find an expression for the derivative of h(x)=ln(f(x)). answer in terms of f and f'.

A: The given function is  h(x) = ln(f(x))

Q: The derivative of the function f(x) = elan(=) + Ve is

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Q: Find the slope of the graph of the function at the given point.                         f(x) = 5 cos…

A: According to the question, we have to find the slope of function fx=5 cosx-9x at the point 0,5. The…

Q: b) Find the derivative f'(x) in the following cases. 5x+1 1. f(x) = 2x-1. 2. f(x) = 3. f(x) = csc x…

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Q: Find the derivatives of the function f for n = 1, 2, 3, and 4. Use the results to write a general…

A: fx=cosxxn When n=1, fx=cosxx Differentiating with respect to x, we get…

Q: Find the 2021st derivative of the following function: y=cos(x) + sin(x) + e* A cos(x) + sin(x) +…

A: Definition used-                         dndxn(cosx)= cos(x+nπ2), dndxn(sinx)= sin(x+nπ2)…

Q: Evaluate the derivatives of the following functions.

A: Given function is fx=cos-11x. To find the derivatives of the function. Solution: Chain rule of…

Q: Q1:- Find the first order derivative of each of the following functions: c) y sin x = x tan y

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Q: Find the SECOND derivative of the given function. (b) g(x) = x+2

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Q: Find the derivative for each function: g(x) = In ( e^x / 1 + e^x )

A: Our Aim is to find the derivative for function given below:-g(x)=lnex1+ex -(i)

Q: Let h be a function that has second derivative (x+ 1) (x – 2) (x + 4)e5 h"(x) Is x=2 the…

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Q: find the second order derivatives of function f(X)  exsinxcos2

A: To find the second derivative of the below function. fx=exsinxcos2x

Q: f(x) = sec(x2 – 1) + tan(x2 – 1)] e(æ+æ)

A: Given function - f(x) = secx2-1+tanx2-1ex2+xDifferentiating on both sides with respect to x -f'(x) =…

Q: Find The Domain of the Function. y = sin(log, x²]

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Q: Find the derivative with respect to x if f(x) = e 2x %3D The derivative with respect to x if f(x) =…

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Q: Use the chain rule to find the derivatives of f(x) and g(x) as well as f'(0) and g'(0): f(x) = (2x³…

A: According tp our guidelines we can solve only one question so we are solving 2nd question for you.…

Q: d -y(x) if e²-y = sin a d.x

A: We will solve the following

Q: Differentiate the following function: (e-*) * y = sec

A: Given: y=sece-x2

Q: Find the first and second derivatives of the following function: g(t) = t°et g'(t) g" (t) =

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Q: Which of the following function has 10" derivative equal to zero? A f(x) =(3x²-4x +2)³ B f(x)…

A: Here we find out whic function 10th derivatives is zero.

Q: g(t) = cosh-1 t3

A: The objective of the question is determine the derivative of the given function.

Q: Let f(x)= e^x^2 . Find an equation of the line tangent to the graph of f at the point the (1,e).

A: Tangent to the graph,

Q: Solve for the derivative of the given functions using the Chain Rule formula. Let f(x) = √(x2 + 3x +…

A: (a) fx=x2+3x+1 Inner function : u=x2+3x+1. Outer function : y=u.

Q: Find the second order derivatives of the following functions f(x) 3x - x' i) Tan 1-3x

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Q: Differentiate the function.

A: Consider the following equation: y=e-2tcos4t Differentiate y with respect to t: dydt=ddte-2tcos4t…

Q: Solve for the derivative of the given functions using the Chain Rule formula.Let g(x) = sin (cos…

A: Since, g(x)=sin (cos x)g'(x)=cos (cos x)ddxcos (x)⇒g'(x)=cos (cos x)(-sin (x))ddx(x)⇒g'(x)=-cos (cos…

Q: Find the first, second, and third derivative of the following function. g(z) = 1

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Q: Find the third derivative f"" for the function f(x) = I-5

A: The first derivative of is given as: Also the derivative of a function in form of is: The given…

Q: Find the following derivative 1 g(x) = 2* · (x² + 1)

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Q: Consider the function g defined by 1 g(x, y) = cos (7x/) - CoS log3(x – y)

A: Given problem:-

Q: Find the derivative. COSx a) f(x) = In %3D x2-4 4 b) g(x) = Vx + e2x + Tt

A: Given : (a) f(x)=ln(cosxx2−4)

Q: Consider the function defined by f (x) = -x + ae" where a E R: (1) find a such that the graph of the…

A: To Determine: Consider the function defined by f(x)=-x+aex-1 where a∈ℝ find a such that the graph of…

Q: 1. Find the derivatives of the following functions: a. g(x) = x ÷ sin(x). 2. Find the derivative…

A: Find the derivatives of the following functions:  a. g(x) = x ÷ sin(x). 2. Find the derivative of…

Q: Find the derivative f'(x) for the function f(x) = x² + x – 17. - O A. f'(x) = 2x – 16 В. f («) — 2а…

A: Find the derivative of f(x)