Question

find the derivative of y=4√x(2x+3) (square root is x only)

Answer 1

rewrite the question using indices

\[y= 4x^{\frac{1}{2}}\times (2x + 3)\]

you could use the product rule at this point or simplify the equation further

using the index law for multiplying same base... add the powers


\[y = 8x^{\frac{3}{2}} + 12x^{\frac{1}{2}}\]

so you should be able to differentiate this

Answer 2

ALright, I get that, however, on our exam, the answer is supposed to be 6(2x+1) all over square root of x, can you find any way to end up with this answer? Every way we've done it has given us a different answer!

Answer 3

ok... so the derivative is

12x^(1/2) + 6x^{-1/2}



or \[12\sqrt{x} + \frac{6}{\sqrt{x}}\]

mutliply each term by

\[\sqrt{x} \]

but I would have thought the simplification would have been

\[\frac{6}{\sqrt{x}}(2x + 1)\]

or

\[\frac{6(2x +1)}{\sqrt{x}}\]

and allowing for the denominator to be rationalised you would have

\[\frac{6\sqrt{x}(2x + 1)}{x}\]