The above is the graph of the derivative f '(x). How many critical points does the original function f(x) have?

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

A:

Q: Find the second derivative for the functions defined as follows g(x) = 4x(ln x)

A: We have to find second derivative of the function: gx=4x lnx Since two function are in product so we…

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.

A: Given function is By using the properties of logarithm, ln(a/b)=ln(a)-ln(b) and ln(a^b)=bln(a), we…

Q: Find the derivative of the function. y = tan an-¹ (√x-4)

A: We can find the derivative using chain rule as below.

Q: Find the derivative of f( x ) = 2° log3(z + 2.5) f'(x) =

A: The first derivative of the function is . The product rule of the differentiation is .

Q: Find the derivative of function.

A: The given function is f(x) = ln(xex+2).We have to find the derivative of this function with respect…

Q: Find the derivative. h(x) = In(cosh(7x)) h'(x) =

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Q: Find the thousandth derivative of  f(x)  = x e-x

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Q: find the derivative of y with respect to the givenindependent variable.

A:

Q: What is the first derivative of s(x) = 4e.

A: Given function - s(x) = 4ex-3Differentiating on both sides with respect to x - ddxs(x) =…

Q: L(x) = In(x)+log,(x)

A: Used formulas : ddx(logax) = 1x ln a ln x = loge xloge e = ln e = 1ln 5 =1.61

Q: y = In- e 2x+1

A:

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 the function. h(x) = x2 arctan(5x)

A: Given function: hx=x2tan-15x Differentiate the above function w.r.t "X" h'x=ddxx2tan-15x

Q: Find the derivative of f(x) = Inx + 1].

A: f(x) = ln [x2x2+1]f'(x) = ddx[ ln [x2x2+1] ]f'(x)= 1 x2x2+1 ddx[x2x2+1]

Q: Here is the graph of the second derivative of a function g(x). g"(x) Where does g(x) have a point of…

A: Inflection point is at that x value where the double derivative of the function is 0.

Q: Find the derivative of the function f(x) = coth−1(x2)

A:

Q: 2) Find nth derivative of the following function f(x) = ex

A: Given query is to find the nth derivative of the expression.

Q: Suppose that the second derivative of the function y=f(x) is y'' = (x-3)(x+9). For what x-values…

A:

Q: Find all possible functions f with the given derivative. f'(x)= 1/x-1, x is greater than 1

A: Obtain the all possible functions as follows.

Q: If C(x)=x' + x°, evaluate the fourth derivative at x = 2. %3D

A: To find the fourth derivative of the function: C(x)=x5+x-3 at x=2

Q: 26 Find the 155th derivative of (1 + x°)" at x = 0.

A: see 2nd step.

Q: p(x) = In(x)^/x

A:

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: 1 Find the function whose derivative is (x+1)-

A:

Q: Suppose that the second derivative of the function y = f(x) is y" = x*(x = 2)°(x + 3). For what…

A: Given: The second derivative of the function y=f(x) is y"=x2(x-2)3(x+3) Definition: The inflection…

Q: 3/x +1 f(x) = X+2 at x = -1

A:

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

A: This question is based on chain rule differentiation.

Q: Suppose that the second derivative of the function y = ƒ(x) is y′′ = (x + 1)(x - 2). For what…

A: For inflection point we must have y" = 0

Q: What is the Derivative of the following function;  y = Arctan 2(x 3)

A: To find: The derivative of y=tan-1x32. Formula used: Chain rule of derivative: fgx'=f'gx·gx Power…

Q: Let f (x) = 7 cos(Tx). Find the twentieth derivative of f (x).

A:

Q: Find the derivative of the function. f(x) = arctan(3x)

A: We  can make it easier for you.

Q: Which of the following has a derivative of f (x) = 2x (arctanx + arccotx)?

A:

Q: Find the first derivative of the function of f(x) using any method?

A: Given,

Q: 5) Explain why the definition of a numerical derivative does not exist at x = 2 in the graph shown.…

A: The objective is to explain the reason definition of numerical derivative doesn't exist at x=2 in…

Q: What role does the denominator of f'(x) play in finding the critical points (in other words, what do…

A: The given data is: f'x

Q: 1. Y= 3x -x- 2

A: Find your answer below

Q: Find the derivative of the function h(x) = x2 arctan5x

A: The given function is h(x) = x2 arctan5x

Q: Find the 4th derivative of x^10 evaluated at x=0. What would be the 100th derivative of x^2000 be at…

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Q: Find the derivative of the following using the three-step rule 2. y=Va² +x

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Q: Find the derivative of the function.   y = In(x)/x9

A:

Q: Find the thousandth derivative of f(x) = xe -x

A: Given function,  f(x) = xe-x  To find the thousandth derivative of f(x)

Q: find the derivative of y with respect to the givenindependent variable. y = log2 5θ

A:

Q: Find the derivative of the function. x + 4 f(x) = In X – 4 | f'(x) =

A:

Q: find the derivative of y with respect to the givenindependent variable. y = log5 ex

A: On simplification, we get

Q: Find all possible functions with the given derivative. = రx = 1x 2x

A: The answer is given below

Q: Suppose that the second derivative of the function y = ƒ(x) is y'' = x2(x - 2)3(x + 3). For what…

A: Given that, y=f(x) Second Derivative is y'' = x2(x - 2)3(x + 3). As we know that, Inflection point…

Q: Find the derivative of the function. h(x) = ets. - x + 1

A: Differentiate w.r.t x