Prove that the derivative of an even function is an odd function and then of an odd function is an even function

Q: In , the derivative of the function has the same sign for all x in its domain, but the function is…

A: The given function is fx=xx2-4. Sketch the graph of function fx=xx2-4 as shown below.

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: Let f be a differentiable even function. By use of the definition of the derivative directly, prove…

A: AS we know what are even and odd function. Even Function  f(-x)=f(x) Odd Function f(-x)=-f(x)

Q: se part one of the fundamental theorem of calculus to find the derivative of the function. g(x) (x)…

A: We have to find derivative

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)>0    We first find the zeros of f'(x) They are x=-1 , 3, 6

Q: Let f(x)=," 1 Use the definition (first principle) to determine the 1-x derivative of ƒ(x).

A:

Q: let f(x) be a function such that its derivative is given by: f'(x)=5(x-1)^2(x-2)^3(x-3)^4. which…

A: Consider the graph of given first derivative: If the graph of f '(x) changes from negative to…

Q: Use the definition of a derivative to find f'(x) and f"(x). f(x) = 3x2 + 2x + 2 f'(x) = f"(x) =…

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Q: According to a web page on the internet, the derivative of a pro derivatives: in other words,…

A: Given fx=8x+7gx=3x+4

Q: x4 -5 7) f(x) = In %3D

A: fx=lnx4-5x first, simplify the function  f(x)=lnx4x-5x f(x)=lnx3-5x now take derivative

Q: Find the derivative of the function g(x) et 5x - g'(x) =

A: We have to use quotient rule for derivative and use  d/dx(ex)=ex d/fx(ax+b)=a

Q: Use the definition of a derivative to determine all points for the function f(x) = ((x+|x|)^2)+1 is…

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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: sketch the graph of a function f whose derivative f' has the given description:f'(x) > 0 for x…

A: Given that f'(x) > 0 for x > 3 and f'(x) < 0 for x < 3. There are many possible graph to…

Q: 1 . Use the definition of the derivative to compute f'(x) if f(x)

A: We use the limit definition of f'(x)

Q: compute the derivative. f (x) = esin2x

A: Differentiation of the function with respect to x helps to find the derivative of the function. The…

Q: sketch the graph of a function f whose derivative f' has the given description. f'(x) > 0 for x…

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Q: What is the derivative of the following function?

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

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

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Q: Give the derivative formula for the function. g(x) = 2.1* + g'(x) =

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

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

Q: The product rule states that the derivative of a product of functions f (x) and g (x) is equal to f…

A: Let h(x) = f(x) * g(x)

Q: The graph below is of f "(x) for some function f(x) with domain (-∞, ∞) (i.e., the graph of of the…

A: Since you have asked a question with multiple question in a single request, we would be answering…

Q: Sketch the graph of derivative of given functions.

A: Given graph of function is,

Q: 3. Give a sketch of the function using the information provided in the given derivative map.

A: we can see graph

Q: Give algebraic proofs that for even and odd functions:(a) even times even = even; odd times odd =…

A: We say that a function f(x) is even if f(-x)=f(x) We say that a function f(x) is odd if f(-x)=-f(x)

Q: (*) 5

A: We know that derivative of xn is nxn-1. Here We use fundamental theorem of calculus then find g'(x).…

Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. g(x) =…

A:

Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. (t - g'(s)…

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Q: Sketch a graph of the first and second derivative for the function f(x) shown:

A: Solution is given below:

Q: :) Given f(x) = |x|+x, at which point does the derivative not exist? Mathematically Question 4 (-…

A: We are given a function fx=x+x and we have to find the point at which fx is not derivable. We know…

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: 1 Use the definition of derivative to find the derivative of the function f()

A: Solution:

Q: -3 Let f(x) %3D (a) Using the definition of derivative, show that the derivative is f'(x)

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Q: ). Prove that the derivative of an even function is odd and that the derivative of an odd function…

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Q: Every elementary function has an elementary derivative.

A: The elementary functions can be a constant, sum/difference of two elementary functions, product,…

Q: If a function is increasing everywhere (and it has a derivative), then it's derivative function is…

A: explanation of above question is given below,

Q: determine whether each staement is true or false "every elementary function has a an elementary"…

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Q: Find the derivative of the following function by definition (from first principle): f(X)=1-x/2x

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

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Q: find the derivative of the function:   f(x) = det [ -1  -4  3  -4  -3 ]                  [  3   0…

A: To Determine: find the derivative of the function that is f'(x) Given we have a determinate…

Q: Find the derivative of (x+5) / (x2-1) with respect to x.

A: Here we have to use formula of derivative  dxndx=nxn-1

Q: Use the definition of a derivative to show that if f(x) = 1/x, then f'(x) = -1/x². (This proves the…

A: Given: fx=1x

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

A:

Q: Estimate the derivative of the function f (x) =: -3 at the point a = 3.

A: The function is given by fx=x3-3 differentiate the above function w.r.t "x" f'x=ddxx3-3…

Q: Use the Fundamental Theorem of Calculus to find the derivative. g'(x). of the unction

A: Use simple method of funda mental theorem

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: