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Find (dy)/(dx) if y=sin^3xcos^2x...

Find (dy)/(dx) if
`y=sin^3xcos^2x`

Text Solution

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`y=sin^3xcos^2x`
`thereforedy/dx=sin^3x.d/dx(cos^2x)+cos^2x.d/dx(sin^3x)`
`=sin^3x.(2cosx).d/dx(cosx)+cos^2x.3sin^2x.d/dx(sinx)`
`=2sin^3xcosx(-sinx)+3sin^2xcos^2x.cosx`
`=-2sin^4x.cosx+3sin^2xcos^3x`
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