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 2 years ago
Use logarithmic differentiation to find the derivative of the function y = (cosx)^x
 2 years ago
Use logarithmic differentiation to find the derivative of the function y = (cosx)^x

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mf1021
 2 years ago
Best ResponseYou've already chosen the best response.3take the log both sides. lny=xln(cosx)

mf1021
 2 years ago
Best ResponseYou've already chosen the best response.3and take derivative both sides

mf1021
 2 years ago
Best ResponseYou've already chosen the best response.3y prime/y= (ln(cosx))+x(1/cosx)(sinx) and isolate y prime and you are done

robtobey
 2 years ago
Best ResponseYou've already chosen the best response.0\[\int\limits \text{Cos}[x]^x (\text{Log}[\text{Cos}[x]]x \text{Tan}[x])dx = \text{Cos}[x]^x \]

Ayesha1603
 2 years ago
Best ResponseYou've already chosen the best response.0put ln on both sides to get \[\ln y =x \ln cosx\] then differentiate to get \[1/y =1\times sinx\]

Sarkar
 2 years ago
Best ResponseYou've already chosen the best response.0also you can use formula for logarithmic differentiation... d/dx(u^v)=u^v*d/dx(v*log u )
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