If f(x)=∫[1,x^2] t^t dt

find f'(x).

Another problem similar to this one on my assignment was f(x)=∫[1,x] t^t dt, and the answer was f'(x)=x^x. That same pattern would say this answer should be (x^2)^(x^2), but that's not being accepted. What am I missing here? Please help

1 answer

You forgot the chain rule. The result is

(x^2)^(x^2) * 2x

if f(x)=∫[1,u] t^t dt
and u = u(x) then
f'(x) = f(u) * du/dx
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