Question

Find the derivative of y = x^x

Answers

Count Iblis
Hint: Write x^x as exp[x log(x)]
Steve
if u and v are functions of x, and

y = u^v
y' = vu^(v-1) u' + lnv u^v v'
= u^v (v/u u' + lnv v')

sort of a combination of the power rule and the exponent rule.

Count Iblis's suggestion is also useful, and can be done by noting that

ln y = x logx
1/y y' = 1 + logx

Related Questions