Mathematics
washingtonsharda
22

Find the derivative of f(x)=4.15cos^x

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(1) Answers
testuser07

Did you mean the derivative of (cos x)^x ? Then, use logarithmic differentiation: y = (cos x)^x ln(y) = ln[(cos x)^x] ln(y) = x * ln[cos x] (1/y) * y' = 1* ln[cos x] + x * (-sin x)/(cos x) y' / y = ln[cos x] - (x sin x)/(cos x) y' = y* [ ln[cos x] - (x sin x)/(cos x) ] the key step in the process - the substitution. You had: y = (cos x)^x, so we will substitute for y. y' = (cos x)^x* [ ln[cos x] - (x sin x)/(cos x) ] (and this is your final answer)

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