Question

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

Answer 1

`2x^4-2x^3-8`

`2*4x^3-2*3x^2-0`

`8x^3-6x^2`

Answer 2

`dy/dx=8x^3-6x^2`

Explanation:

`"differentiate using the "color(blue)"power rule"`

`•color(white)(x)d/dx(ax^n)=nax^(n-1)`

`dy/dx=8x^3-6x^2-0=8x^3-6x^2`

Answer 3

`y'=8x^3-6x^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=nx^(n-1)`

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

`color(blue)(y'=8x^3-6x^2)`