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

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Answer 1 · 2015-08-10T17:24:11

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

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

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

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

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

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