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

1 Answer
Cesareo R.
Jun 3, 2016

#(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)#

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