What is the derivative of #x^(cosx)#?

1 Answer
Jun 3, 2016

Answer:

#(dy)/dx = x^{cos(x)} (cos(x)/x - sin(x) log_e x)#

Explanation:

#y = x^{cos(x)} equiv log_e y = cos(x) log_e x#
Deriving the log transformed equation we have
#dy/y = -sin(x)log_e x dx+cos(x)/x dx#
grouping
#(dy)/dx = y(cos(x)/x - sin(x) log_e x)#
and finally
#(dy)/dx = x^{cos(x)} (cos(x)/x - sin(x) log_e x)#