Question #88d66

1 Answer
Oct 21, 2014

#y=x^{x^2}#

By taking the natural log,

#Rightarrow lny=lnx^{x^2}#

by the log property #ln x^r=rln x#,

#Rightarrow lny=x^2 lnx#

by differentiating implicitly,

#Rightarrow {y'}/y=2xcdotlnx+x^2cdot 1/x=(2lnx+1)x#

by multiplying by #y=x^{x^2}#,

#Rightarrow y'=(2lnx+1)x^{x^2+1}#.


I hope that this was helpful.