# How do you differentiate f(x)=5x^4-3x^2+2?

Apr 12, 2015

Use three properties of derivatives:

The derivative of a sum (or difference) is the sum (or difference) of the derivatives.
This tells us that we can find the derivatives of each term seperately and add(subtract) the derivatives.

The derivative of a constant time a function is the constant times the derivative.
This tells us that the coefficients will simply multiply the derivatives of the variable factors.

The power rule tells us the the derivative of ${x}^{n}$ is $n {x}^{n - 1}$.
(You con include the derivative of a constant is $0$.)

So:

$f \left(x\right) = 5 {x}^{4} - 3 {x}^{2} + 2$.

$f ' \left(x\right) = 5 \left(4 {x}^{3}\right) - 3 \left(2 {x}^{1}\right) + 2 \left(0\right)$.
So,

$f ' \left(x\right) = 20 {x}^{3} - 6 x$.