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Answer 1 · 2017-04-09T19:14:43

I'm assuming your question is:

What's #dy/dx# when #y=(x+1)^(x^2)#?

#y=(x+1)^(x^2)#

Take the natural logarithm of both sides:

#ln(y)=ln((x+1)^(x^2))#

#ln(y)=x^2ln(x+1)#

Differentiate both sides.

#1/ydy/dx=2xln(x+1)+x^2/(x+1)#

#dy/dx=y(2xln(x+1)+x^2/(x+1))#

#dy/dx=(x+1)^(x^2)(2xln(x+1)+x^2/(x+1))#