What is the derivative of $(ln x) ^ cos x$ ?

Question

4515 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-06-27T16:50:28

$(lnx)^cosx ( -sinx ln lnx + cosx /(x lnx))$

Let $y=(ln x)^cos x$ , so that ln y= cos x ln ln x

Now differentiate both sides,

$1/y dy/dx = -sinx ln ln x + cos x 1/lnx 1/x$

$dy/dx= (lnx)^cosx ( -sinx ln lnx + cosx /(x lnx))$

What is the derivative of (ln x) ^ cos x(ln x) ^ cos x?