Quandaries and Queries


Hello! It's me again, Cher

I have another problem with regards to the derivative, what about the derivative of x to the power x?




Hi Cher,

Finding the derivative of xx depends on knowledge of the natural log function and implicit differentiation.

Let y = xx. If you take the natural log of both sides you get

y = xx then
ln(y) = ln(xx) = x ln(x)

Now differentiate both sides with respect to x, recalling that y is a function of x.

 1/y y' = ln(x) + x 1/x = ln(x) + 1


y' = y(ln(x) + 1) = xx( ln(x) + 1)




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