Question

Differentiate f(x) = x^x

Answer 1

f(x)' =x(x)^x-1

Answer 2

how did u get that eyad?

Answer 3

f(x) = x^x
Let f(x) = y
y = x^x
lny = x*lnx
Then take derivative of both side:
y'/y = lnx + 1
y' = y(lnx+1)
Substitute y back in from original equation:
y' = x^x(lnx+1)

Answer 4

@ryman : its a law ,, if u got an (x) powered with a number , then its derivative = let the number get down next to the x ,and subtract from the power one . :)

Answer 5

You can't use the power rule in this case. You have to solve it by implicit differentiation.

Answer 6

but the power is not a number its a variable

Answer 7

multiply both sides by y (or x^x) to get y'