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?

Cher

Hi Cher,

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

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

y = x^x then
ln(y) = ln(x^x) = 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

Thus

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

Penny

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