Question

Find the derivative of the function y=ln (1+e^x/ 1-e^x)

Answer 1

can we use logarithmic properties here?

Answer 2

chain rule

Answer 3

yes, but first we can break it up and make it easier on ourself

Answer 4

ya.it would be better ....using log both side

Answer 5

2e^x/(1-e^2x)

Answer 6

yes

how did you get that

Answer 7

yeah thats the answer but to get there we can write it as:

y=ln(1+e^x)-ln(1-e^x)

Answer 8

Then we differntiate both sides

Answer 9

\[y=\ln(1+e^x)-\ln|1-e^x|=>y'=\frac{(1+e^x)'}{1+e^x}-\frac{(1-e^x)'}{1-e^x}\]

Answer 10

y=sin\[\sqrt[3]{x}\] +\[\ \sqrt[3]{sinx}\]