# Does anybody know how to solve the limit of #(x^x-x^{x^2})/(1-x)^2# when #x->1# ?

##### 1 Answer

-1

warning: long answer

#### Explanation:

plugging

since this is indeterminate form, you can find the derivative of the numerator and divide that by the derivative of the denominator and still have the same limit (L'hopital's rule)

limit is now:

[SIDE NOTE: to find the derivatives of

then use implicit differentiation:

substitute y back in:

do the same for

the limit simplifies to:

plugging in

limit becomes:

(might want to check https://www.derivative-calculator.net/)

plugging in

check with this graph:

graph{(x^x-x^(x^2))/((1-x)^2) [-2.605, 6.165, -2.768, 1.617]}