Question

Does anyone know how to find the derivative of
y=(sqrt(x)) (x+24)

Answer 1

Use the product rule.

Answer 2

\(f(x) = uv\)

\(f'(x) = uv' + vu'\)

Answer 3

I got to (3/2x^1/2)+(12x^-1/2)....does this look right?

Answer 4

\[y=\sqrt{x}\left( x+24 \right)=x ^{\frac{ 3 }{ 2 }}+24x ^{\frac{ 1 }{2}}\]
\[y=x ^{n},\frac{ dy }{ dx }=nx ^{n-1}\]

Answer 5

right and then you would pull the (3/2) in front to get ((3/2)x^(1/2)) and then the 1/2 in front of 24 to get 12x^(-1/2)?

Answer 6

yes ,you are correct.

Answer 7

and then thats the answer? Do I have to simplify it anymore?

Answer 8

no need.

Answer 9

Thank you so much!