The graph of the first derivative f' of a function f is shown. (Assume the function is defined only for 0 < x < 9.)

Q: Sketch the graphs of two functions that have the given derivative: f'(x)=2

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Q: f(x) = (x + 2)2/3 -

A: First we have to find f'(x) . And to find extrema by first derivative test we have to find all roots…

Q: . Find the  n th derivative of each function by calculating thefirst few derivatives and observing…

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Q: Find the derivative of f(x) = 2 tan^-1(x) 6^x

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Q: Define the derivative of f(x) at x

A: Consider a function f(x) The differentiability of a function:  Let f(x) be a real valued function…

Q: Define the derivative of f(x) at x =a

A: For a function f(x), the derivative is defined as: Now at x=a, the derivative is defined as:

Q: Use the graph of the first derivative function  f'(x) to find the interval  on which function is…

A: Given: the graph of the first derivative function  f'(x).

Q: Find f'(x) using the definition of the derivative. 1. f(x)=x^3-1

A: We have given f(x) = x3-1 So using definition of derivative  f'(x) = limh→0fx+h-fxh So f(x+h) =…

Q: Suppose the derivative of a function  f isf'(x) = (x+ 1) 2 (x -3)5 (x -6)4. On what interval f  is…

A: f(x) will be increasing if f'(x)&gt;0    We first find the zeros of f'(x) They are x=-1 , 3, 6

Q: Find the derivative of the function f(x) = arccot √x

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Q: . Find the  n th derivative of each function by calculating thefirst few derivatives and observing…

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Q: Find the second derivative for the functions defined as follows ƒ(x) = (x2 - 1)2

A: Given function: fx=x2-12 fx=x4-2x2+1 Differentiate the equation w.r.t "x"…

Q: 1 ソ= 1- x

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Q: Sketch the graph of the derivative for function shown.

A: Graph has a horizontal tangent between x=-2 and x=-1, at x=0 and at x=2.9, Therefore graph of f'…

Q: Find the derivative of f(x) = Vx-7 tan-(x) + In a- 2.

A: We have to find the derivative of the function f(x)=x-7tan-1x+lnx-2.

Q: Sketch the graph of the derivative for function shown.

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Q: Match the graph of the above function with the graph of its derivative. 0 ㅇ O 수 +

A: The given graph of the function is the graph of a semi circle. Or positive side of the circle.

Q: f(x) = Vet + evi

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Q: Use the fact that the derivative of the function ​f(x)=4/x is f"(x)=-4/x2 to find the equation of…

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Q: Use the fact that the derivative of the function g(x)=√x is g"(x)=1/2√x to find the equation of the…

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Q: Sketch the graph of the derivative for function shown.

A: Plot the derivative for -∞&lt;x&lt;0. The function f(x) is constant in the interval -∞&lt;x&lt;0 so…

Q: Suppose the derivative of the function y = ƒ(x) is y′ = (x - 1) 2(x - 2)(x - 4). At what points, if…

A: It is given that, the function f(x) has the derivative

Q: Given the derivative f'(x), find the x-value for all relative extreme for the graph of the original…

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Q: Suppose 8 (x) =sec='(x<). what is the derivative of g with respect to x?

A: We can find the answer as below.

Q: The first derivative of the function h is given by h' (x) = x³ – 3x2 + x. What are all intervals om…

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Q: Give a justified example of function f(x) that is differentiable everywhere, yet its derivative has…

A: Definition of Differentiability p(x) is said to be differentiable at the point x = b if the…

Q: 1. Evaluate the derivative of f (x)= sec(In(x²)). DO NOT SIMPLIFY.

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Q: Given f(x) = 2, find f' (1) using the definition of a derivative. x-2 Provide your answer below:…

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Q: find the function with the given derivative whosegraph passes through the point P. g'(x) = 1/x2 +…

A: g'(x)=1x2+2x,P(-1,1) Formula ∫xndx=xn+1n+1+C

Q: State the formula for the definition of the derivative of a function f (x) provided x is any number…

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Q: Which of the following statements is true about the function f whose derivative is f'(x) = (x – 1)(x…

A: Given :   Find inflection point equate to zero

Q: Find the derivative of the function. f(x) = In x+ 2 f'(x) =

A: We have to find the derivative of the given function.

Q: Suppose the derivative of f is f '(x)=- At what values of x does the f does have a x slope of -4.

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Q: f(x)

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Q: Find the derivative of f(x)=x^1/2 at x=1/144

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Q: Let f(x) = 4x + . Use the definition of the derivative to find f'(1).

A: Solve

Q: What is the derivative of f(x) = (tan^-1)((3+x)/(1-3x))

A: Given:f(x)=(x+3)arctan(x)1-3xf'(x)=ddx(x+3)arctan(x)1-3x=ddx(x+3)arctan(x)·(1-3x)-(x+3)arctan(x)·ddx…

Q: 13. Sketch the derivative f'(x) for this graph of f (x):

A: Graph drawing of f'(x) problem...

Q: Find f (x) of f(x)= by using the definition of the x- derivative.

A: Definition of Derivative is given as

Q: Sketch the graph of the function f whose derivative has the given graph

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Q: Sketch the graph of a function whose derivative satisfies the properties given in the following…

A: Graph

Q: If f(x) = sec (x) tan(x), then a particular anti-derivative of f(x), is -csc (x) + 1.

A: Firstly we have to find the antiderivative of function f(x)=secx tanx.then given the statement

Q: Find the derivative of f(x) = cot^−1(x^2 + 3)

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Q: Suppose the first derivative of a function is f'(x) = (x- 30)(19x+ 1). The function f is decreasing…

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Q: Find the derivative of the following function, where x is already declared as a symbolic variable: f…

A: We have to find the derivative of the given function…

Q: Use the definition of derivative to compute f '(0). e-1/x if x * 0 if x - 0 f(x) f '(0) -

A: The definition of the derivative is given by: f'(x)=limh→0f(x+h)-f(x)h⇒f'(0)=limh→0f(h)-f(0)h  ...…

Q: Find the derivative of the following function by definition (from first principle): f(x) = x-1

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