- #1

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## Homework Statement

Differentiate the following function: [tex]f(x) = x\sqrt{x^{3}+2x}[/tex]

## Homework Equations

N/A

## The Attempt at a Solution

Here's my attempt:

First I rewrite it as:

[tex]f(x) = x(x^{3}+2x)^{\frac{1}{2}}[/tex]

Now, I differentiate using chain rule:

[tex]f(x) = x(3x{^2}+2x)(\frac{1}{2})(x^{3}+2x)^{\frac{1}{2}-1}[/tex]

By simplifying and rearranging the equation, I get:

[tex]f(x) = \frac{3x^{3}+2x}{2\sqrt{x^{3}+2x}}[/tex]

But, this what my book got:

[tex]f(x) = \frac{3x^{3}+2x}{2\sqrt{x^{3}+2x}} + \sqrt{x^{3}+2x}[/tex]

I checked my answer over thrice just in case I made any minor errors, and I don't think I have. Where did I go wrong? Did I apply the wrong rule? Thanks in advance.