Question

y=cos(x^3) sin^2(x^5)
find dy/dx​

Answer 1

Step-by-step explanation:

What is the derivative of cosx^3*sin^2(x^5)?

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y=cos(x3)sin2(x5)

dydx=ddxcos(x3)sin2(x5)

⟹dydx=sin2(x5)ddxcos(x3)+cos(x3)ddxsin2(x5)

⟹dydx=sin2(x5)(−sin(x3))ddxx3+cos(x3)2sin(x5)ddxsin(x5)

⟹dydx=sin2(x5)(−sin(x3))3x2+cos(x3)2sin(x5)cos(x5)ddxx5

⟹dydx=sin2(x5)(−sin(x3))3x2+cos(x3)2sin(x5)cos(x5)5x4

⟹dydx=−3x2sin2(x5)sin(x3)+10x4cos(x3)sin(x5)cos(x5)