Why can't the power rule be used to differentiate the function y = = e"?

Q: What is the third derivative of 大 f(x): f(r) = 2 + cosx?

A: The given function is fx=x3+cos x. Evaluate the first derivative of the given function as follows.…

Q: what is derivative of f(x)=x/(x+1)^2

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Q: Find the 28th derivative of the function f(x)= cos(x). The answer is function _____

A: The first derivative of sin(x) is cos(x). And the first derivative of cos(x)=-sin(x). Hence, second…

Q: Use the Power Rule to compute the derivative: da x=1

A: Using the power rule for differentiating x4

Q: 1/x using the definition o

A: we have to find the derivative of f(x) using the first principal. f(x)=x+1x

Q: Use Leibniz’s Rule to find the derivatives of the functions

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Q: What is the geometric interpretgtron of the derivative f'(a)?

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Q: Differentiate f(×) = sin x from first principles

A: Given query is to find the differentiation of sin(x) from the first principal.

Q: Find the derivative of the function. Q(x) = V ex + x Q'(x) = %3D

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Q: Find all relative extrema of the function f(x) = x* – 4r +2 by using | the Second Derivative Test…

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Q: Define the second derivative of f. If f(t) is the position  function of a particle, how can you…

A: Second derivative is derivative of the derivative.      Therefore,…

Q: Apply the second derivative test to find all relative extrema. (c) f(x) = 1

A: To find the relative extrema first we  find the critical points. The critical points are the values…

Q: Find the first derivative of f(x) = e3r

A: To find the first derivative of fx=x3e3x. Solution: Quotient rule of derivative states that:…

Q: compute the derivative. f (x) = ex sin x

A: Given: fx=exsinx We know that ddxu.v=vdudx+udvdx                                              ..1

Q: Explain how to apply the Second Derivative Test.

A: The second derivative test is used to find the relative maxima or relative minima. The second…

Q: Find the second derivative of the function.

A: Given: fx=x cosx Now to find the derivative of the given function, Differentiate given function with…

Q: How can linear approximation be used to approximate the changein y = f(x) given a change in x?

A: Given;                 y=fx How can linear approximation be used to approximate the changein y=f(x)…

Q: . Does the function cos x x + 0 f(x) = 0, x = 0 have a derivative at x = 0? Explain.

A: Consider the given function fx=1-cosxx        x is not equal to 0x=0

Q: Why can't the power rule be used to differentiate the function y = e"?

A: Given

Q: Find the derivatives of the function f(x) from the first principle x*+4

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Q: Describe the Second Derivative Test in your own words

A: A second derivative test is conducted to find the relative maxima and  minima of a given function.

Q: Find the second derivative of the function.     f(x) = x cos x

A: Given: fx=xcosx for finding second derivative of given function, we find first derivative then…

Q: 8 Use the power rule to find the derivative of f(x) = x°. f'(x) =

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Q: Determine whether the following statement is true or false, and explain why. The chain rule is used…

A: Given: The chain rule is used to take the derivative of a product of functions.

Q: What are the applications of these derivatives?

A: First derivative tells the rate at which the original function changes.  Second derivative tells the…

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

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Q: Find the second derivative of the function.

A: Given,         f(θ)=3tanθ

Q: What is the derivative of f(x) = tan-(x)? %3D

A: We can solve this as follows:

Q: 6. Use the definition of derivative to find f'(x) if f(x) 3D х2 — Зх — 4

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Q: 5. What is the definition of the derivative of a function f(x) ?

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Q: Differentiate the function (x + y)1/2 = x4 + y4 by implicit differentiation.

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Q: Explain how the Second Derivative Test is used.

A: The second derivative may be used to determine local extrema of a function under certain conditions.…

Q: What is the derivative of y = ekx?

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Q: Find the second derivative of the function. f(x) = sec x * "(x) = Noc

A: Please see the explanation below

Q: 5. f(x)%3D + cos X

A:

Q: Explain why the Second Derivative Test is often mistaken for the POI Test. In what way(s) are they…

A: We know the following. POI Test: An inflection point is a point on the graph at which the second…

Q: What is the derivative of (x^2+1)^x?

A: Use the lograthim to find the derivative of given expression.

Q: How do you find the derivative of the product of two functionsthat are differentiable at a point?

A: Consider the two functions f(x) and g(x). f(x)·g(x)'=f'(x)g(x)+g'(x)f(x). Here f(x)·g(x)' represents…

Q: 10 Use the power rule to find the derivative of f(x) = Vx.

A: Given,          The function is fx=x10 .

Q: Illustrate the Derivative of Cosecant Function ?

A: Illustrate the Derivative of the Cosecant Function?

Q: Find the second derivative of the function f(x) = sec2x

A: Given: f(x)=sec2(x)

Q: Find the derivative of the function f(x) = v4-x2 by definition

A: The given function is f(x)=4-x2 The definition of the derivative is given by: If a function f(x) is…

Q: 13 Use the power rule to find the derivative of f(x) = 'Vx.

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Q: Differentiate the given by implicit differentiation x3 - xy + y3 =1

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Q: w(x) %3D хе*

A: To find the second derivative of function w(x)=xex

Q: How do some functions vary continuously?

A: Given: Behaviour of the functions which vary continuouslyFor instance:…

Q: Find the derivative of f(x) : %3D

A: We need to differentiate the function f(x)=1x with respect to x. We also know that ddxxn=nxn-1.

Q: How do you find the derivative of the quotient of two functions that are differentiable at a point?

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Q: What is the definition of the derivative (Difference Quotient)?

A: 2. What is the definition of the derivative(difference quotient)? ans. In single-variable calculus,…