What is the derivative of (x^3+1)^2?

3 Answers
Mar 31, 2018

color(indigo)(f'(x) = 6x^2 * (x^3 + 1)

Explanation:

f(x) = (x^3 + 1)^2

http://faculty.wlc.edu/buelow/Web%20Library/chain_rule.htmhttp://faculty.wlc.edu/buelow/Web%20Library/chain_rule.htm

Applying the chain rule,

f'(x) = 2 * (x^3 + 1) * (d/(dx)) (x^3 + 1)

f'(x) = 2 * (x^3 + 1) * 3x^2

color(indigo)(f'(x) = 6x^2 * (x^3 + 1)

Mar 31, 2018

6x^5+6x^2

Explanation:

"expand the factor "(x^3+1)^2

rArr(x^3+1)^2=x^6+2x^3+1

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

•color(white)(x)d/dx(ax^n)=nax^(n-1)

rArrd/dx((x^3+1)^2)=6x^5+6x^2

Mar 31, 2018

6x^5+6x^2

Explanation:

Firstly, expand the brackets

(x^3+1)(x^3+1)=x^6+x^3+x^3+1=x^6+2x^3+1

Now take the derivative using the power rule:

d/dx (x^6+2x^3+1)

-> d/dx=6x^5+6x^2

Remembering when deriving, multiply the power by the coefficient, and then -1 from the power.

Also remembering that if there is no x, it cannot be derived