Calculus Question?

Question

What is the derivative of x^x(2x-1)^2

Answer 1

easy

let y = x^ x(2x-1)^2
take product of uv with u = x^x and v = (2x-1)^2 or (4x^2-4x +1)

du/dv = x^x(1+ln x)

dv/dx = (8x-4)

now dy/dx = u dv/dx + v ud/dx
= x^x(8x-4) + (2x-1)^2.x^x(1+ ln x)

Answer 2

This is a weird one.

I'm assuming that your question is f(x) = x ^ [ x ( 2x - 1) ] ^ 2

f'(x) = x ^ [ 2x ( 2x - 1 ) ( 2 ) ]
f'(x) = x ^ ( 8x^2 - 1 )

Answer 3

for hint :
take e^xlnx = x^x

I cant do it without a pen and paper;
sorry :P