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Question
Differentiate the function with respect to x.
`cos x^3. sin^2 (x^5)`
Solution
`cos x^3 . sin^2 (x^5)`
Let y = `cos x^3 . sin^2 (x^5)`
`dy/dx = (d(cos x^3. sin^2 (x^5)))/dx` by quotient rule
`= (cos x^3 d sin^2 (x^5))/dx + (sin^2 (x^5) d cos x^3)/dx` By the chain rule
`= (cos x^3 (2 sin (x^5)). d sin (x^5))/dx + (sin^2 (x^5) (- sin x^3). d x^3)/dx`
`= (cos x^3 (2 sin (x^5)). cos x^5 dx^5)/dx + sin^2 (x^5) (- sin x^3) 3x^2`
`= cos x^3 2 sin (x^5) cos x^5 . 5x^4 + sin^2 (x^5)(- sin x^3) 3x^2`
`= 10 x^4 sin x^5 cos x^5 cos x^3 - sin x^3 sin^2 sin^2 x^5`
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