# Use the product rule to find the derivative?

## $f \left(x\right) = \left(6 \sqrt{\left(x\right)} - 2\right) \left(5 \sqrt{x} + 7\right)$

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#### Explanation

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#### Explanation:

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Mar 8, 2018

$\frac{d}{\mathrm{dx}} \left(g \left(x\right) \cdot h \left(x\right)\right) = g ' \left(x\right) \cdot h \left(x\right) + h ' \left(x\right) \cdot g \left(x\right)$

#### Explanation:

Here ,
g(x) = (6√x−2)
h(x) = (5√x+7)

$g ' \left(x\right) = \frac{3}{\sqrt{x}}$
$h ' \left(x\right) = \frac{5}{2 \cdot \sqrt{x}}$

by product rule:

 d/dxf(x) =(6√x−2)*5/(2*sqrt(x)) + (5√x+7)* 3/sqrt(x)

$\implies \frac{3 \left(5 \sqrt{x} + 7\right)}{\sqrt{x}} + \frac{5 \left(6 \sqrt{x} - 2\right)}{2 \sqrt{x}}$

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