Question

how do u find the derivative of a square root function

Answer 1

ex: f(x)=ln (square root x^2-3)

Answer 2

Just convert the square root to a 1/2 power and use the power rule.

Answer 3

f'(x) = u'/ u

Answer 4

ok so i get up to putting xponent in front and then i get confused

Answer 5

you subtract 2/2 from the exponent

Answer 6

\[\frac{d}{dx}\sqrt{x}=\frac{1}{2\sqrt{x}}\]
then by the chain rule
\[\frac{d}{dx}\sqrt{f(x)}=\frac{f'(x)}{2\sqrt{f(x)}}\]

Answer 7

do not use the stupid power rule, simply memorize this one

Answer 8

lol stupid power rule =))

Answer 9

the square root is a very common function, so you simply need to know it without resorting to rules. like knowing that \(8\times 7=56\)
you will see it lots, so don't waste your time finding it each time
plus math teachers love to put in on tests, so JUST KNOW IT

Answer 10

especially since it never changes.

Answer 11

your problem however is different. you have
\[\ln(\sqrt{x^2-3})=\frac{1}{2}\ln(x^2-3)\] so derivative does not require the rule for square roots. just requires remembering that
\[\frac{d}{dx}\ln(f(x))=\frac{f'(x)}{f(x)}\]

Answer 12

but what if it's cube root x..what then

Answer 13

so in your case you get
\[\frac{1}{2}\frac{2x}{x^2-3}=\frac{x}{x^2-3}\]\]

Answer 14

if it is the cube root then i suppose if you do not remember that
\[\frac{d}{dx}\sqrt[3]{x}=\frac{1}{3\sqrt[3]{x^2}}\] then go ahead and use the power rule, it always works, but the square root you should memorize

Answer 15

hm well yeah i agree with that..after all for me sqrt x is automatic...i think it should be for you (asker) as well

Answer 16

think of the time you will save on an exam when everyone else is writing
\[\sqrt{x}=x^{\frac{1}{2}}\]
\[\frac{d}{dx}x^{\frac{1}{2}}=\frac{1}{2}x^{\frac{1}{2}-1}=\frac{1}{2}x^{-\frac{1}{2}}=\frac{1}{2\sqrt{x}}\]