Question

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

Answer 1

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

Explanation:

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

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)`

Answer 2

`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`

Answer 3

`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