# How do you differentiate y= 2x^4 - 2x^3 - 8?

May 31, 2018

$2 {x}^{4} - 2 {x}^{3} - 8$

$2 \cdot 4 {x}^{3} - 2 \cdot 3 {x}^{2} - 0$

$8 {x}^{3} - 6 {x}^{2}$

May 31, 2018

$\frac{\mathrm{dy}}{\mathrm{dx}} = 8 {x}^{3} - 6 {x}^{2}$

#### Explanation:

$\text{differentiate using the "color(blue)"power rule}$

•color(white)(x)d/dx(ax^n)=nax^(n-1)

$\frac{\mathrm{dy}}{\mathrm{dx}} = 8 {x}^{3} - 6 {x}^{2} - 0 = 8 {x}^{3} - 6 {x}^{2}$

May 31, 2018

$y ' = 8 {x}^{3} - 6 {x}^{2}$

#### Explanation:

The key to differentiating polynomials is using the Power Rule. Here, the coefficient comes out front, and the exponent gets decremented by one. Here's how this looks mathematically:

${x}^{n} = n {x}^{n - 1}$

Also recall that the derivative of a constant is zero. Applying this, we get

$\textcolor{b l u e}{y ' = 8 {x}^{3} - 6 {x}^{2}}$