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

3 Answers
May 31, 2018

#2x^4-2x^3-8#

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

#8x^3-6x^2#

May 31, 2018

#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#

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)#