Question

derivative of 1/(sqrt(2x^2 - 1)

Answer 1

what is the derivative of \(\frac{1}{\sqrt{x}}\) ?

Answer 2

x^-1

Answer 3

sms can you work with me pls?

Answer 4

x^-1/2

Answer 5

oh yeahh

Answer 6

Lets rewrite the equation in that form. easier to visualize

Answer 7

ok

Answer 8

\[x ^{\frac{ -1 }{ 2 }}\rightarrow -\frac{ 1 }{ 2 }x ^{-\frac{ 3 }{ 2 }}\]

Answer 9

same derivative rules apply. bring the exponent out front and subtract 1 from the exponent

Answer 10

this problem differs in that you also need to multiply it by the dervative of what is inside the ( )

Answer 11

see what you get

Answer 12

helps to write
\[-\frac{1}{2}x^{-\frac{3}{2}}=-\frac{1}{2\sqrt{x^3}}\]

Answer 13

I would wait to rewrite it until the very end, after you have taken the derivative of the inside.

Answer 14

rational exponents are helpful when finding derivatives, but you need to figure out what you really get at the end.
now you can use the chain rule. since you see the derivative of
\[\frac{1}{\sqrt{x}}\] is
\[-\frac{1}{2\sqrt{x^2}}\] you know that the derivative of
\[\frac{1}{\sqrt{f(x)}}\] is \[-\frac{f'(x)}{2\sqrt{f^3(x)}}\]

Answer 15

How are you doing Jay

Answer 16

the derivative of the inside is 4x^3 right?

Answer 17

or you could do whats @smstevns said if it makes it easier for you

Answer 18

remember it is minus 1

Answer 19

no it is \(4x\)

Answer 20

satellite proved the theorem for you to remember in the future

Answer 21

this is what you need to write
\[-\frac{f'(x)}{2\sqrt{f^3(x)}}\] replace \(f(x)\) by \(2x^2-1\) and replace \(f'(x)\) by \(4x\)

Answer 22

It can be simplified from there depending on what your teacher is looking for. -4x/2 = -2x

Answer 23

simplifying the numerator

Answer 24

i see sorry

Answer 25

Hope we helped. peace