f and g are the functions whose graphs are shown, and h(a) = f(x)g(x), find h' (2). %3D

Q: In Example 6 in this section, we were given f(x) = 3x2 + 2x + 11 and found f '(x) = 6x + 2. (a)Find…

A: We have to given that f(x)=3x2+2x+11 and f'(x)=6x+2. It is known that rate of change is given as…

Q: (x+3)° 3. Use logarithmic diffrentiation to find the derivative of y' =- (1+2}(r+4}

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Q: 3. Find the first and second derivatives of the function f (x) = e¬²

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Q: To find the revenue function, we integrate the marginal revenue function. In this case we can use…

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Q: Find the equation of the line tangent to the graph of f at the indicated value of x. f(x) = In x;…

A: Determine the derivative for f(x). fx=lnx5f'x=ddxlnx5=ddx5lnx5×ddxx5=1x5×5x4=5xSo, f'x=5x

Q: (x+3)² (x+2)°(x+4)' Use logarithmic differentiation to find the derivative of y =

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Q: Sketch the graph of the function y=|ln|x||.

A: Given:  Function y=f(x) = |ln|x|| To Find: Graph of function f(x) Concept used: Consider the graph…

Q: Find the first derivative of each function. a) f(x)=ln (e^x+e^-x)

A: “Since you have asked multiple questions in a single request, we will be answering only the 1st…

Q: 5. Use logarithmic differentiation to find the derivative of these functions. (a) y = /Te* (x² +…

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Q: 5. For y = -ln(x), find the value of x where the slope is a) x = − 6 b) -In(6) d) Does Not Exist

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Q: 1) Find the derivative of the function g(x) = (arctan x)3, first showing how to get the d formula…

A: As per guideline we have solve only one question

Q: The derivative of the function y = log2(In(x)) is: 1 1 y': x In 2 In x y' = x In 3 ln x the above…

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Q: Higher and Implicit Differentiation y= x5 -3√x+1/x5, Find d5y/dx5

A: Given the function,  y = x5 - x3 +1x5 We can rewrite the function y = x5 - x13 + x-5 Here,  using…

Q: The derivative of the function f(x) =x ln x is: a. f'(x) = In x +1 b. f'(x) = ln x +. c. f"(x)= In x…

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Q: In the left-hand column below are graphs of two functions. In the right-hand columns are graphs of…

A: When function is increasing its derivative is positive but when function is decreasing ,its…

Q: 3) Use logarithmic differentiation to find the derivative of the function a) y = Vxe&(x? + 1)" Your…

A: We have to find derivative

Q: Find the derivative of the exponential function. y = e5x tan(5x)

A: given that  y =e5x  tan(5x)  So dy/dx=e5x d/dx(tan 5x)+tan (5x). d/dx(e5x)                 i.e…

Q: Find the average rate of change of y = log1/2 x over the interval 1 < x < 4. Write your answer as a…

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Q: Find the equation of the line tangent to the graph off at the indicated value of x. 6 3 f(x) = Inx;…

A: In this question we have to find the equation of the line tangent to the graph of f at the indicated…

Q: (b) Sketch the graph of f (x) = ln(4 – x²). Use the first and second derivatives to identify where…

A: Consider the function  fx=ln4−x2

Q: 6) Consider the exponential function f (x) = ex* [C:4] a) Determine the n-th derivative of f(x). b)…

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Q: f(x)=ln(1+x/1-x) is function even or odd

A: We have to find the given function is either even or odd: fx=ln1+x1-x We know that for even function…

Q: x is a function of g. find dx/dg if given glnx = tanx2 - eg

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Q: The graph of the derivative of a function is given. y For which x is the (original) function…

A: The graph of the derivative (f') of the graph f is given. Now, the original function f is increasing…

Q: Note, derivative of a logarithmic function f(x) has three parts and is given here: f ' (x) = 1/ln…

A: We know that loga u(x) can be written as : logau(x) = (ln u(x)) / (ln a) = p(x)

Q: The half-life of a radioactive material is the time required for an amount of this material to decay…

A: Given,

Q: Vx+2 Use logarithmic differentiation to find the derivative of the function. f(x)=- e (3x-1) i ora…

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Q: Find the equation of the line tangent to the graph of f(x) = (In x)? at x= 8.

A: f(x)= (lnx)2

Q: What is the relationship between the functions In r and e?

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Q: If x moves from a to a nearby value a + dx, how do you estimate the corresponding change in the…

A: First of all, consider a differential function f (x).Consider two points a and a + dx on x axis.The…

Q: find the extreme values on the interval f (x) = x − 12 ln x, [5, 40]

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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: e +e Differentiate y = -x- e -e

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Q: A graph of y = f(x) is shown. In the same coordinate system, sketch a graph of the derivative…

A: here x-intercepts are x=-3 and x=1 so the factored form of the parabola is…

Q: Find all the relative and absolute extrema of the given function on the given domain f(x) = x^2 +…

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Q: A radio active element (x) has a half-life of 38 hours. Initially, X = X0 %3D . Determine the amount…

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Q: Find exact value(s) for x such that 3e" - e' = 0.

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Q: C) Find the derivative of y= (1+ x²)* D) Find the derivative of f(x) = log3 5x? + 1

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Q: (0. §) Find the equation of the function f whose graph passes through the point and whose derivative…

A: you can clearly understand if you follow the below solution

Q: Consider a revenue function defined as 200e0.4x R(x) = 1 + x It can be shown that R' 0. What is the…

A: Given Revenue function, Rx=200e0.4x1+x To check which of the following statements are true. In order…

Q: Homogenous function dy/dx = y(lny - lnx +1)/x

A: To Determine :-  Homogeneous solution  dydx = y ln y - ln x +1x

Q: 3. Find all possible functions with the given derivative y' =- 2

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Q: A model used for the yield Y of an agricultural crop as a function of the nitrogen level N in the…

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Q: A function f(x) is defined by f(x) ce Find the value of the constant e for (x) dx=1.

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Q: A culture initially has N0 number of bacteria. At time t = 1 hour the number of bacteria is measured…

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Q: y = log,((2x³ – x² + 7)(x² + 4)) %3D -

A: Please see the solution below

Q: differentiate the function: y= 13/ln(x) y'=

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Q: y' of y = *(1-x²)² (1+x²)7 using logarithmic differentiation

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Q: 5. Use logarithmic differentiation to find y' for y = (V)5*, Simplify as much as possible.

A: Giveny=(x)5x To find y'

Q: Find the average rate of change of the function f(x) = = læ + 0x + 8, on the interval x E [-2,0].…

A: Given:fx=x2+8  on the    interval -2,0Average rate of change of the functionAx=fb-fab-aa=-2 , b=0