# How do you differentiate f(x)=7x^3-x^2+x using the sum rule?

Apr 6, 2018

$f ' \left(x\right) = 21 {x}^{2} - 2 x + 1$

#### Explanation:

$\frac{d}{\mathrm{dx}} \left(7 {x}^{3} - {x}^{2} + x\right) = \frac{d}{\mathrm{dx}} 7 {x}^{3} - \frac{d}{\mathrm{dx}} {x}^{2} + \frac{d}{\mathrm{dx}} x$, we can break up a derivative across sums or differences.

Thus,

$f ' \left(x\right) = \left(3\right) \left(7\right) {x}^{2} - 2 x + 1$

$f ' \left(x\right) = 21 {x}^{2} - 2 x + 1$