# How do you differentiate f(x)=1/3(2x^3-4) using the product rule?

Sep 4, 2016

$f ' \left(x\right) = 2 {x}^{2}$

#### Explanation:

The product rule is not required here as there is not a product of 2 functions.

The $\textcolor{b l u e}{\text{product rule}}$ is used in the following situation.

$f \left(x\right) = g \left(x\right) . h \left(x\right)$

here $f \left(x\right) = \frac{2}{3} {x}^{3} - \frac{4}{3} \text{ distribute the bracket}$

now differentiate using the $\textcolor{b l u e}{\text{power rule}}$

That is color(red)(|bar(ul(color(white)(a/a)color(black)(d/dx(ax^n)=nax^(n-1)" and " d/dx("constant")=0)color(white)(a/a)|)))

$\Rightarrow f ' \left(x\right) = \left(3 \times \frac{2}{3}\right) {x}^{2} - 0 = 2 {x}^{2}$