How do you differentiate y= 2x^4 - 2x^3 - 8y=2x42x38?

3 Answers
May 31, 2018

2x^4-2x^3-82x42x38

2*4x^3-2*3x^2-024x323x20

8x^3-6x^28x36x2

May 31, 2018

dy/dx=8x^3-6x^2dydx=8x36x2

Explanation:

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

•color(white)(x)d/dx(ax^n)=nax^(n-1)xddx(axn)=naxn1

dy/dx=8x^3-6x^2-0=8x^3-6x^2dydx=8x36x20=8x36x2

May 31, 2018

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)