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Differentiate the following functions...

Differentiate the following functions with respect to `(x^2+2)/(sqrt(cosx))`

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Verified by Experts

Here, we will use,
`(u/v)' = (u'v-v'u)/v^2` Let `y = (x^2+2)/(sqrtcosx)`
Differntiating both sides w.r.t. `x`,
`dy/dx = ((2x)sqrt(cosx) - (1/(2sqrtcosx))(-sinx)(x^2+2))/cosx`
`=>dy/dx = (4xcosx+sinx(x^2+2))/(2cosxsqrtcosx)`
`=>dy/dx = (2x)/sqrtcosx +(tanx(x^2+2))/(2sqrtcosx)`,
which is the required solution.
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