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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)#

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