Question

Determine the derivative of the following and leave the answer with positive exponents
Ay/ax if y=5x+√x to the exponent 5/2x²

Answer 1

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))]