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Find derivative of cos(logx+e^x) , x >0 ...

Find derivative of `cos(logx+e^x)` , `x >0` w.r.t. to `x`

Text Solution

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`"Let" y = "cos" ("log" x +e^(x))`
`rArr (dy)/(dx) =(d)/(dx)"cos" ("log" x + e^(x))`
`=-"sin"("log" x + e^(x))(d)/(dx)("log" x +e^(x))`
`=-"sin"("log" x +e^(x))((1)/(x)+e^(x))`
`=(-"sin" ("log" x + e^(x))(1 + x * e^(x)))/(x)`
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