d/dx(cos(x))^(1/x)

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1 Answer

Let y=(cos(x))^(1/x), then ln(y)=(1/x)ln(cos(x)).

Differentiate:

(1/y)dy/dx=(1/x)(-sin(x)/cos(x))-(1/x²)ln(cos(x)),

dy/dx=-(1/x)[(cos(x))^(1/x)][tan(x)+(1/x)ln(cos(x))].

by Top Rated User (1.2m points)

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