The table below shows values of differentiable functions, f (x) and g(x), and their derivatives at selected values of x. Use the table of values below to answer each of the questions below. f'(x) g'(x) a. Approximate the value of f'(1.5). Explain why your answer is a good approximation of f'(1.5). f(x) 3 3 g(x) 2 -1 2 3 -3 2 5 3 1 -2 3 10 4 -1 b. If B(x) = /g(x), what is the equation of the tangent line drawn to B(x) when x = 1? c. If A(x) = x² In(f(x)), what is the value of A'(2)? What does this result say about the behavior of the graph of A(x) when x = 2? Give a reason for your answer.

Q: Find the derivative of h(x) = | 14 arctan(t) dt. h'(x) = ||

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Q: find the derivative of y with respect to the appropriatevariable. y = sin-1 3/t2

A: We differentiate with respect to t using chain rule.

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. y = In(t2) – arctan 3 y' =

A: It is derivative.

Q: Find the derivative of the following functions using the long method (limits) (a) x =t-5t- 3 (b) y =…

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Q: find the derivative of y with respect to x, t, orθ, as appropriate.

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Q: Find the derivative of y with respect to x. 1 y=x' In (x)---x obra d we do O A. 7x5-x² OB. 8x5-x2…

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Q: Find the value of the derivative (if it exists) at each indicated extremum.           f(x) = cos x/2

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Q: find the derivative of y with respect to x, t, orθ, as appropriate. y = e(cos t + ln t)

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Q: find the derivative of y with respect to x, t, orθ, as appropriate. y = esin t(ln t2 + 1)

A: The variable is t in this equation  So we will differentiate with respect to t   We will use the…

Q: The function f(r) = tanh(r) is one-to-one and so is invertible. Using our rule/ formula for relating…

A: Given that

Q: Find the derivative of the function below. F(x) = arctan e a*) f'(x) =

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Q: eリ- + 2y eTy x° +

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Q: Find the derivative of the function.

A: We have a nested form of functions . We have to use chain rule of differentiation to find the…

Q: find the derivative of y with respect to the appropriatevariable. y = s√(1 - s2) + cos-1 s

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Q: Can you help me step by step?

A: Differentiate with respect to x,

Q: Find the derivative of y with respect to x, t, or 0, as appropriate. 16) y = (x2 - 2x + 1) eX B) (x2…

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Q: Compute the high-accuracy central difference approximation for the first derivative of y = cos x at…

A: There are three types of approximations to the derivative of a function f(x) at a point a. They are…

Q: find the derivative of y with respect to x, t, or θ, as appropriate. y = t (ln t)2

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Q: Find the derivative at the given point. f(x)= at x = 0 %3D x+1 O 1/4 O-1

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Q: The derivative of the function 3+ln x is: y = cos(In x)

A: y=3+ln(x)cos(ln(x)Differentiate w.r.t.xApply the Quotient Rule:  fg'=f…

Q: find the derivative of y with respect to x, t, or u,as appropriate. y = 1 + ln t/1 - ln t

A: The given function is y=1+ln t1-ln t

Q: Consider the derivative function h (x) = -sec? (x) + 9. What is the general antiderivative of h?

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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 of the given functions. f(x) = 5 ln x   f'(x)= ? g(x)= ln (x^5). g'(x)= ?

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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 y with respect te X /3 %3D

A: Finding dy/dx

Q: 1+ cos x y = In 1-cos x

A: This question is based on chain rule differentiation.

Q: Find the second derivative 1. y = In(x^3+1) 2. y = Arctan (e^x)

A: Given: y=lnx3+1, y=tan-1ex

Q: find the derivative of y with respect to x, t, or θ, as appropriate.

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Q: find the first order derivative of the function

A: We have to solve

Q: Find the derivative for x+1 a)f(x)=- x-4 b)f(x)= sin' 2x Show the work on your notebook, take a…

A: (a) To find: The derivative of fx=x+1x2-4. Formula used: Quotient rule of derivative:…

Q: find the derivative of y with respect to x, t, or θ, as appropriate. y = ln (t3/2) + √t

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Q: find the derivative of y with respect to the appropriatevariable. y = (θ2 + 2θ) tanh-1 (θ + 1)

A: The given function is y=θ2+2θ tanh-1θ+1. Obtain the derivative as follows.

Q: Give the derivative of f(x) arctan an(e³*) at the point where x = 0.

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Q: y = e* - cos 3x + xlog.(1+x)

A: By using some formula of derivative

Q: To begin with, calculate the first derivative f'(x) = Now use this derivative to find the critical…

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Q: Can you help me step by step with this problem?

A: Differentiate both sides w.r.t. x.And for addition we can apply the derivative separately on both…

Q: y = e* arctan x y = arccsc (e*) ICCSC

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Q: Find the derivative of f(x) and solve for x sinx a. f(x) X = 6. b. f(x) e* sinx X = 0 COSX c. f(x) X…

A: Given: (1) f(x) = sin x / x  at x = π/6  (2).  f(x) = ex sinx at  x= 0 (3).  f(x) =  cos x / ex   at…

Q: Use the alternative form of the derivative to find the derivative at x = c (if it exists). (If the…

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Q: The derivative of xª at x = e is equal to .Soloot ono

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Q: The derivative of the function y 1 = COS Va at a = 0 is equal to

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Q: How do you solve question 10?

A: Given function is  By definition of derivative , we have

Q: i. y = cosh(2x – 1) %3D 1 j. y = arccosh H| 8

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Q: Find the derivative of y with respect to the given independent variable. e* cos' x (1) y= x+1

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Q: Use backward, forward , and centered difference approximation to estimate the second derivative of…

A: The formulas for the backward, forward, and central differences to approximate the second derivative…

Q: 11 with respect to x is The derivative of y = cos - 1

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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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Statements and Logic

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