Use logarithmic differentiation to find the derivative of the function.

Question

y =sqrt(x)^3x

Answer 1

y = (√x)^3x
lny = 3x ln√x = 3/2 x lnx
1/y y' = 3/2 (lnx + x/x) = 3/2 (lnx + 1)
y' = 3/2 y (1+lnx)
= 3/2 (√x)^3x (1+lnx)
= 3/2 x^(3x/2) (1+lnx)