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Question Number 125165 by Mammadli last updated on 08/Dec/20
f(x)=sinx^(cosx) f ′(x)=?
f(x)=sinxcosxf′(x)=?
Answered by Dwaipayan Shikari last updated on 08/Dec/20
f(x)=(sinx)^(cosx) log(f(x))=cosxlog(sinx) ((f′(x))/(f(x)))=−sinxlog(sinx)+((cos^2 x)/(sinx)) f′(x)=(sinx)^(cosx) (log((1/((sinx)^(sinx) )))+(sinx)^(cosx−1) cos^2 x
f(x)=(sinx)cosxlog(f(x))=cosxlog(sinx)f′(x)f(x)=−sinxlog(sinx)+cos2xsinxf′(x)=(sinx)cosx(log(1(sinx)sinx)+(sinx)cosx−1cos2x

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