Ask your own question, for FREE!
Mathematics
OpenStudy (anonymous):

use logarithmic differentiation to find y=(x^2 = 1)^x

myininaya (myininaya):

i don't get the equation.

OpenStudy (anonymous):

y = (x^2 + 1)^x sorry about typo

myininaya (myininaya):

take ln of both sides

myininaya (myininaya):

\[\ln(y)=\ln(x^2+1)^x\]

myininaya (myininaya):

\[\ln(y)=x \ln(x^2+1)\]

myininaya (myininaya):

take derivative of both sides: \[\frac{y'}{y}=1 \ln(x^2+1)+x \frac{2x}{x^2+1}\]

myininaya (myininaya):

not multiply both sides by y

myininaya (myininaya):

\[y'=y(\ln(x^2+1)+\frac{2x^2}{x^2+1})\]

OpenStudy (anonymous):

wait how did you get the 1ln(x^2 +1).....

myininaya (myininaya):

\[y'=(x^2+1)^x(\ln(x^2+1)+\frac{2x^2}{x^2+1})\]

myininaya (myininaya):

i used product rule

myininaya (myininaya):

\[(x \ln(x^2+1))'=(x)'\ln(x^2+1)+x[\ln(x^2+1)]'\]

myininaya (myininaya):

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

OpenStudy (anonymous):

okay I multiplied by y, now how can I simplify it?

Can't find your answer? Make a FREE account and ask your own questions, OR help others and earn volunteer hours!

Join our real-time social learning platform and learn together with your friends!
Latest Questions
klmjnmkj: math problem
2 minutes ago 3 Replies 0 Medals
TurtlePrincess: Explain some of the beneficial results of well-written sentences.
6 minutes ago 0 Replies 0 Medals
klmjnmkj: math problem
5 minutes ago 14 Replies 1 Medal
klmjnmkj: math problem
23 minutes ago 10 Replies 1 Medal
hiimamazon: hai im amazon
28 minutes ago 3 Replies 0 Medals
LmaoKylee: hello
29 minutes ago 10 Replies 0 Medals
TETSXPREME: help i forgot how 2 do this xd
9 minutes ago 28 Replies 5 Medals
Can't find your answer? Make a FREE account and ask your own questions, OR help others and earn volunteer hours!

Join our real-time social learning platform and learn together with your friends!