# Find: What is the derivative of (10x^2+1)e^{3x}

## Question:

What is the derivative of {eq}(10x^2+1)e^{3x} {/eq}

## Derivative:

If we have the product of two functions say u and v then to differentiate it we will use the product rule and then rearrange to get the derivative.

## Answer and Explanation:

To find the derivative we will use the product rule:

{eq}\frac{\mathrm{d} uv}{\mathrm{d} x}=uv'+u'v {/eq}

Now using the product rule we will differentiate:

{eq}f(x)=(10x^{2}+1)e^{3x} {/eq}

Differentiating it we get:

{eq}f'(x)=3e^{3x}(10x^{2}+1)+e^{3x}(20x)\\ =e^{3x}(30x^{2}+3+20x) {/eq}

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Solving Partial Derivative Equations

from GRE Math: Study Guide & Test Prep

Chapter 14 / Lesson 1
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