# How do you differentiate f(x)= 7xsinx using the product rule?

Feb 5, 2016

$f ' \left(x\right) = 7 \sin x + 7 x \cos x$

#### Explanation:

The product rule states:

$f \left(x\right) = g \left(x\right) h \left(x\right) \to f ' \left(x\right) = g ' \left(x\right) h \left(x\right) + g \left(x\right) h ' \left(x\right)$

So for $f \left(x\right) = 7 x \sin x$ we can take:

$g \left(x\right) = 7 x$ and $h \left(x\right) = \sin x$

Thus $g ' \left(x\right) = 7$ and $h ' \left(x\right) = \cos x$

Substituting this into the product rule:

$f ' \left(x\right) = 7 \sin x + 7 x \cos x$