y= (cosx)^x

logarithmic differentiation to find derivatived of function

y= (cos x)^x
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1 Answer

y=cosx(x), so:

ln(y)=xln(cos(x)).

Differentiate:

(1/y)dy/dx=-xsin(x)/cos(x)+ln(cos(x))=-xtan(x)+ln(cos(x)),

dy/dx=y(-xtan(x)+ln(cos(x)))=cosx(x)(ln(cos(x))-xtan(x)).

by Top Rated User (1.2m points)

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