## anonymous 4 years ago Use logarithmic differentiation to find the derivative of the function y = (cosx)^x

1. anonymous

take the log both sides. lny=xln(cosx)

2. anonymous

and take derivative both sides

3. anonymous

y prime/y= (ln(cosx))+x(1/cosx)(-sinx) and isolate y prime and you are done

4. anonymous

$\int\limits \text{Cos}[x]^x (\text{Log}[\text{Cos}[x]]-x \text{Tan}[x])dx = \text{Cos}[x]^x$

5. anonymous

put ln on both sides to get $\ln y =x \ln cosx$ then differentiate to get $1/y =1\times -sinx$

6. anonymous

also you can use formula for logarithmic differentiation... d/dx(u^v)=u^v*d/dx(v*log u )