Question

How do you find the derivative of `(x^4 - 1)^10 (2x^4 + 3)^7`?

Answer 1

`56x^3(x^4-1)^10(2x^4+3)^6+40x^3(2x^4+3)^7(x^4-1)^9`

Explanation:

Use the product rule :
`d/dx(f(x)*g(x))=f(x)*g'(x)+g(x)*f'(x)`

and inside this product rule there will be need for use of the power rule :
`d/dx[u(x)]^n=n*[u(x)]^(n-1)*(du)/(dx)`.

Hence the derivative of the given function with respect to x is :

`(x^4-1)^10*7(2x^4+3)^6*(8x^3)+(2x^4+3)^7*10(x^4-1)^9*(4x^3)`

`=56x^3(x^4-1)^10(2x^4+3)^6+40x^3(2x^4+3)^7(x^4-1)^9`.