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Question
Differentiate the function with respect to x.
cos x3 . sin2 (x5)
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Solution
Let, y = cos x3 . sin2 (x5)
`dy/dx = d/dx [cos x^3. sin^2 (x^5)]`
= `cos x^3 d/dx sin^2 (x^5) + sin^2 (x^5) d/dx cos x^3`
= `cos x^3 . 2 sin (x^5) d/dx sin (x^5) + sin^2 (x^5) (- sin x^3) d/dx (x^3)`
= `cos x^3 . 2 sin (x^5) cos (x^5) d/dx (x^5) + 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)`
= `10x^4 cos x^3 sin(x^5) cos(x^5) - 3x^2 sin^2(x^5) sinx^3`
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