Can someone please help me with this Calculus problem?

Question

Use logarithmic differentaion to find the derivative of the following:

y = (cos x)^x^5

(that's (cos x) raised to the x^5)

I would really appreciate some help. Thanks.

Answer 1

y = (cos x)^x^5
ln y = ln ((cos x)^x^5)
ln y= x^5 ln (cos x)
taking the derivative...

1/y= (x^5)*(1/(cos x))*(-sin x) + ln (cos x) * 5*x^4
1/y= (x^5)*(1/(cos x))*(-sin x) + ln (cos x) * 5*x^4

Answer 2

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