Possible derivation:
d/dx(log(x^(4 x)))
Simplify log(x^(4 x)) using the identity log(a^b) = b log(a):
= d/dx((4 x) log(x))
Factor out constants:
= 4 (d/dx(x log(x)))
Use the product rule, d/dx(u v) = v ( du)/( dx) + u ( dv)/( dx), where u = x and v = log(x):
= 4 log(x) (d/dx(x)) + x (d/dx(log(x)))
The derivative of x is 1:
= 4 (x (d/dx(log(x))) + 1 log(x))
The derivative of log(x) is 1/x:
= 4 (log(x) + 1/x x)
Simplify the expression:
Answer: |= 4 (1 + log(x))
