Consider the parent function, f(x)=/ x. Identify any translation and reflection shifts needed to graph g(x) = -/(x - 5) + 8.

Q: Moreover, suppose F(x) = f(g(x)) and G(x) = g(f(x)). Use the chain rule to calculate the following…

A: f(x)=cot x  and  g(x)=5x-2

Q: Find the derivative of function defined as follows.

A: Given:  y = 6x4 - 2x3 + 5x+ 3To Find:  Derivative of y that is dydxSolutionWe will find the dydx by…

Q: Find the derivatives of the functions in Exercise

A: Given :                                  y =9x2+2x2+3To find :…

Q: Use Version 2 of the Chain Rule to calculate the derivatives of the following functions.

A: y=57x3+1-3

Q: use the chain rule to find the derivative of the following function: f(x)=10cos^3(4x)

A:

Q: Find derivatives of the functions defined as follows: y = 73x+1

A: y=73x+1ory=73x·7ory=7·73x Use formula of derivative ddxax=axln a

Q: Find the derivatives of the functions in Exercises s = cos^4 (1 - 2t)

A: The given function is s=cos4 1-2t. Obtain the derivative as follows.

Q: Find an equation of the tangent line to the graph of f at the given point.         f(x) = (x − 4)(x2…

A: Given, The function, f(x) = (x − 4)(x2 + 6x − 1).

Q: Find the derivatives of the functions in Exercise

A: Given function is: ft=t2-1t2+t-2⇒ft=t+1t-1t-1t+2⇒ft=t+1t+2

Q: Compute the derivatives at the given value of a g(x)=(3x-5)/(x-2)     a=1

A:

Q: Find the derivative of fG Cos' (3x²) 2. %3D

A: Consider the given function:…

Q: Find derivatives of the function defined as follows. y = 1.2e5x

A: Given: y = 1.2e5x

Q: write the function as a composite f (g(x)) and compute the derivative using the Chain Rule. y = (x +…

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: Find derivatives of the function defined as follows. y = 5e-4x

A:

Q: If f(x)=sqrt x, find the linearization L(x) at a=4. Thus the graph of L(x) would be tangent to f(x)…

A: Given information: fx=x ,  at a=4 Formula of Linearization  Lx=fa+f'ax-a

Q: Find the derivatives of all orders of the functions in Exercises

A:

Q: Find the equation of the tangent line to the graph of the function g(x)=2x-1/3x+1 at x=0.

A:

Q: Find derivatives of the functions defined as follows: y =(3x3 - 4x)e-5x

A: Given:          y=3x3-4xe-5x Let:  y=f(x)=3x3-4xe-5x Product rule of differentiation is given by…

Q: 5x f(x)= x²-2

A: We have to find the equation of tangent line of the given function. So first of all we will find…

Q: Find the linear approximation of the function g(x) = 1+x at a = 0 and use it to approximate the…

A: We will find g'(x) using the power rule

Q: Find the dy/dx of the following function using Chain Rule. y=(-5x3 - 3)3

A: Find the dy/dx of the following function using Chain Rule.

Q: Find an equation of the tangent line to the graph of the function at the given point.

A: Our Aim is to find an equation of the tangent line to the graph of the function f(x)=e-x-6-(i) at…

Q: Find the derivatives of the following functions using CHAIN RULE. y=(5x + 1)2

A:

Q: Find the derivatives of the functions in Exercise

A: y=x+1x+2x-1x-2

Q: sketch the shifted exponential curves y = 1 - ex and y = 1 - e-x

A: Given  The parent exponential function y=1-ex . To find the graph of the exponential function…

Q: Find derivatives of the function defined as follows. y = x2e-2x

A: The derivative of a product of functions can be calculated using the product rule. Product rule of…

Q: Find the derivatives of the functions in Exercise

A: Given: y=x2+1x+5+1x Differentiating y with respect to x, dydx=ddxx2+1x+5+1x+ddxx+5+1xx2+1…

Q: Find an equation of the tangent line to the graph of Y = e2x-3 at the point (3/2,1).

A:

Q: Find an equation of the tangent line to the graph of the function f(x) = esec(x) at the point (*,…

A: We have to find the equation of tangent line to the graph of function fx=esecx at the point π4, e2.…

Q: Determine the equation of the tangent line of the given function: f(x) = 3x² – 2x; (-1,5) y = -8x-3…

A:

Q: Find the derivatives of the functions in Exercise

A: Explanation: Given that,  w=(2x-7)-1(x+5)     Formula used: According to the product rule of…

Q: Find an equation of the line tangent to the graph of f at the given point.

A: Solution:Given          f(x)=sec-1(ex);              (ln 2, π/3)To find the equation of the line…

Q: Find an equation of the tangent line to the graph of the function at the given point. f(x) =  3x…

A: Point of tangency = (2, 8)m = slope of the tangent line = f'(x) at the point of tangency =…

Q: Suppose that f(x)=4x(1−5x)^4 Find an equation for the tangent line to the graph of ff at x=2

A:

Q: Find derivatives of the functions defined as follows: y = -16e2x+1

A: Derivative of eax  is aeax  So,

Q: Find derivatives of the functions defined as follows: y = 4-5x+2

A: Given: y=4-5x+2

Q: y 3 + 4x-1 = 8y¬1

A: Using differentiation formula:ddxxn=n.xn-1

Q: Find the equation of the tangent line to the graph of x³ + y³ – 3xy = 0 at the 3 3 point ).

A:

Q: Find derivatives of the functions defined as follows: . y = -8e3x

A: Given: y = -8e3x Formula used: If f(x) is any function and k is a constant then ddxkf(x)=kddxfx…

Q: 3 y = In(3 + x) + 3+x' (-2, 3)

A:

Q: Suppose that the graph of the velocity function of a particle is as shown in the figure, where t is…

A:

Q: Find an equation of the tangent line to the graph of y = g(x) at x = –1 if g(-1) = 5 and g' (-1) =…

A: Concept: The Equation of tangent to the graph y = g(x) at point (x1,y1) is given by: (y -y1) =…

Q: Find an equation of the tangent line to the graph of the function (x)= Vx –7 at the point (23, 4).

A:

Q: a derivative computation using the FTC and the chain rule t): df 13

A: Given : ddxFx3 =ddx∫13x3e-t2dt

Q: Suppose f(5) = 2, f'(5) = 8, and g(x) = In [f(x)+4]. Find an %3D equation of the tangent line to…

A:

Q: Find an equation of the tangent line to the graph of the function at the given point, y = e3x−x2,…

A: Given equation: y=e3x-x2 The equation of the tangent passing through the point x1,y1 on the curve…

Q: Find an equation of the tangent line to the graph of the function at the given point. y = 5x−2, (2,…

A: Find an equation of the tangent line to the graph of the function at the given point. y = 5x−2, (2,…

Q: Find derivatives of the functions defined as follows: y = 4e2x2-4

A: We have  y=4e2x2-4 Then, dydx=d4e2x2-4dx=4de2x2-4d2x2-4.d2x2-4dx=4e2x2-44x=16xe2x2-4

Q: y у%3D 4x2 — 2х + 3

A: Using the definition of derivative,

Q: Find an equation of the tangent line to the graph of f at the given point. y = x3 - 3x + 1, (3, 19)…

A: