Question

How do you find the derivative using the power chain rule of `y=(cos(x^4)+x^3))^8`?

Answer 1

`8(cos x^4 +x^3)^7 *(3x^2 -4x^3 sin x^4)`

Explanation:

`dy/dx = 8 (cos x^4 +x^3)^7 d/dx (cos x^4 +x^3)`

= `8(cos x^4 +x^3)^7 * (d/dx cosx^4 +d/dx x^3)`

=`8(cos x^4 +x^3)^7 *(-sin x^4 4x^3 +3x^2)`

=`8(cos x^4 +x^3)^7 (3x^2 -4x^3 sin x^4)`