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Differentiate e^sinx+(tanx)^x with respe...

Differentiate `e^sinx+(tanx)^x` with respect to x.

Text Solution

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`e^(sinx)+tanx^(x)`
different with respect to x
`d/dx(f_1)=e^(sinx)*cosx`
`log(f_2(x))=log(tanx)^x`
`1/(f_2(x))*f_2(x)=log(tanx)+x/tanx*sec^2x`
`f_2'(x)=(tanx)^x[log(tanx)+(xsec^2x)/tanx]`
`f'(x)=f_1'(x)+f_2'(x)`
`f'(x)=e^(sinx)*cosx+(tanx)^x[logtanx+(xsec^2x)/(tanx)]`.
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