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

1 Answer
Aug 10, 2015

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)