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$ f"(x) = 2x + 3e^x $

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$$f(x)=\frac{x^{3}}{3}+3 e^{x}+c x+d$$

01:15

Fahad Paryani

Calculus 1 / AB

Calculus 2 / BC

Chapter 4

Applications of Differentiation

Section 9

Antiderivatives

Derivatives

Differentiation

Volume

Campbell University

Baylor University

University of Michigan - Ann Arbor

University of Nottingham

Lectures

04:35

In mathematics, the volume of a solid object is the amount of three-dimensional space enclosed by the boundaries of the object. The volume of a solid of revolution (such as a sphere or cylinder) is calculated by multiplying the area of the base by the height of the solid.

06:14

A review is a form of evaluation, analysis, and judgment of a body of work, such as a book, movie, album, play, software application, video game, or scientific research. Reviews may be used to assess the value of a resource, or to provide a summary of the content of the resource, or to judge the importance of the resource.

00:33

Find $f^{\prime}(x)$.$…

01:17

Find $f^{\prime \prime}(x)…

00:56

Find $f$ . $f^{\prime …

01:23

Find $f$$$f^{\prime \p…

01:40

Find $f^{\prime}(x)$ if $f…

01:03

01:25

Find $ f'(a) $.

01:39

Find $f$.$$f^{\pri…

00:50

01:28

Given $f(x)=x^{2}+3 x-2,$ …

Find $f^{\prime}(x)$ and s…

So here, given um F double prime of X as to X plus three E D X. Yeah. Yeah. We want to find F prime of X and F ultimately so F prime of X is going to be the anti derivative of two acts, which is X squared plus the anti derivative of three E V X, which is just three E X. Then we want to find F of X which is equal to, we know that the anti derivative of X squared is going to be X cubed over three. And the anti derivative of free E to the X is once again going to be three E to the X. But we have to remember those constant values. So when we took the first anti derivative we would get plus C, which means here for our second anti derivative would get plus C. X. And then plus another constant D. So this right here would be our final answer.

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