Question

Let h(x)= (sqrtx)(f(x)). If f(2) =5 and f'(2) = -3, find h'(2)

Answer 1

\[g(x)=\sqrt{x}f(x)\] right?

Answer 2

or rather \(h(x)\) no matter
use the product rule to find the derivative, then plug in the numbers

Answer 3

you got the derivative?

Answer 4

so it would be (x^1/2)(f(x)) + F'(x)(sqrtx) and I just plug in the numbers it gave me?

Answer 5

no

Answer 6

the derivative of \(\sqrt{x}\) is not \(x^{\frac{1}{2}}\)

Answer 7

\(x^{\frac{1}{2}}\) is the same as \(\sqrt{x}\) written in exponential notation (which is no help)
you need the derivative of \(\sqrt{x}\),
do you know it?

Answer 8

no I don't can you explain how to get it?

Answer 9

yes, you memorize it
\[\frac{d}{dx}\sqrt{x}=\frac{1}{2\sqrt{x}}\]

Answer 10

you can if you like rewrite \(\sqrt{x}=x^{\frac{1}{2}}\) and then take the derivative using the power rule
it is dumb to do it this way, because the square root if a very common function, so it is much better just to know it
like knowing \(9\times 8=72\)

Answer 11

also math teachers love using it on tests and quizzes
while your colleagues are wasting their time using the power rule, go right to the answer you have memorized
much quicker and easier

Answer 12

That made this problem a lot easier to understand thanks I got it from here !

Answer 13

yw