Question

i need help solving this. please :)

y=log(base 5) sqrt x^2-1

Answer 1

solve for what?

Answer 2

you have it solved for y in terms of x already

Answer 3

i need to find the derivative

Answer 4

\(y=\log_5(\sqrt{x^2-1})\)?

Answer 5

then we use the chain rule on the log function

\(\frac{dy}{dx}=\frac{1}{\ln(5)\sqrt{x^2-1}}*\frac{d}{dx}(\sqrt{x^2-1})\)

You with me?

Answer 6

@dolphins121

Answer 7

uhm okay. yeah i think so

Answer 8

is this the function

\(y=\log_5(\sqrt{x^2-1})

\)

Answer 9

oh

Answer 10

that was a question

Answer 11

Is this the function \(y=\log_5(\sqrt{x^2-1})

\) ?

Answer 12

just remember

\[\log _{b}(x) = \frac{ \ln(x) }{ \ln(b) }\]

ln(b) is a constant

Answer 13

or even better \((\log_b(x)'=\frac{1}{\ln(b)x}\)

Answer 14

The answer is

\[\frac{ x }{ \ln(5)*(x^2 +1) }\]

For something to work towards.

Answer 15

\[\frac{ d }{ dx }\log _{5}(\sqrt{x^2 +1}) \]

Answer 16

\(\frac{dy}{dx}=\frac{1}{\ln(5)\sqrt{x^2-1}}*\frac{d}{dx}(\sqrt{x^2-1})=\frac{1}{\ln(b)\sqrt{x^2-1}}*\frac{1}{2\sqrt{x^2-1}}*2x=\frac{2x}{2\ln(b)\sqrt{x^2-1}^2}=\\\frac{x}{\ln(b)(x^2-1)}

\)

Answer 17

does this make sense @dolphins121 ?

Answer 18

yeah that is the function

Answer 19

okay so i don't understand where the 2 came from

Answer 20

which one?

The one on the bottom or the one on the top?

Answer 21

the one on the bottom

Answer 22

& when in the second step why did u change ln(5) to ln(b)?

Answer 23

the derivative of \(\sqrt{x} \) is \(\frac{1}{2\sqrt{x}}\)

Answer 24

oh okay

Answer 25

\(\sqrt{x}\rightarrow x^\frac{1}{2}\rightarrow \frac{1}{2}x^{\frac{1}{2}-1}=\frac{1}{2x^\frac{1}{2}}\)

Answer 26

yes i understand now thanks.

Answer 27

wait uhm so for the final answer why isn't (x^2-1) squared anymore? and why did u take it out of the square root symbol?

Answer 28

@zzr0ck3r

Answer 29

\(\sqrt{x^2-1}*\sqrt{x^2-1}=(\sqrt{x^2-1})^2=x^2-1\)

Answer 30

ohh okay yeah that makes sense thank u

Answer 31

np