# How do you differentiate g(x) = (5x-2)(x^2+1) using the product rule?

Feb 6, 2016

$g ' \left(x\right) = 2 x \left(5 x - 2\right) + 5 \left({x}^{2} + 1\right)$

#### Explanation:

differentiation using the product rule

If g(x) = f(x).h(x)

then g'(x) = f(x).h'(x) + h(x).f'(x)................(A)

here f(x) =(5x - 2 ) and f'(x) = 5
$\textcolor{b l a c k}{\text{-------------------------------------}}$

h(x) $= \left({x}^{2} + 1\right)$ hence h'(x) = 2x
$\textcolor{b l a c k}{\text{--------------------------------}}$

substituting these values into (A)

g'(x) = (5x - 2).2x + $\left({x}^{2} + 1\right) .5$

$\Rightarrow g ' \left(x\right) = 2 x \left(5 x - 2\right) + 5 \left({x}^{2} + 1\right)$