Moleporocky247 Moleporocky247

02-06-2016
Mathematics

Answered

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

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

Verified Answer :

02-06-2016

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= 5xln(5x+√x)+2.5x²1/(5x+√x) (5+1/(2√x))

y'=(5x+√x) ^(2.5 x²)[5xln(5x+√x)+2.5x²1/(5x+√x) (5+1/(2√x))]

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