Determine the derivative of the following and leave the answer with positive exponents

Ay/ax if y=5x+√x to the exponent 5/2x²

Hello,

It was a long time i have done this.

y = (5x+√x) ^ (2.5 x²)

ln y = 2.5x² ln (5x+√x)

We use:

d (ln y) / dx=1/y * dy/dx

y'/y = 5x*ln (5x+√x) + 2.5x²*1 / (5x+√x) * (5+1 / (2√x))

y' = (5x+√x) ^ (2.5 x²) * [5x*ln (5x+√x) + 2.5x²*1 / (5x+√x) * (5+1 / (2√x)) ]