# `y = (ln(x))^cos(x)` Use logarithmic differentiation to find the derivative of the function.

*print*Print*list*Cite

Expert Answers

hkj1385 | Certified Educator

given:

`y = (lnx)^cosx`

taking log both sides we get

`lny = cosx*{ln(lnx)}`

Differentiating both sides we get

`(1/y)*dy/dx = -sinx*{ln(lnx)} + {cosx/(x*lnx)}`

`or, dy/dx = y*[-sinx*{ln(lnx)} + {cosx/(xlnx)}`

`or, dy/dx = (lnx)^cosx[-sinx*{ln(lnx)} + {cosx/(x*lnx)}]`