Hi, can i ask what is the differentiate of #(e^x + e^-x) / (e^x - e^-x)#? Please Thanks much
2 Answers
The derivative is
Explanation:
Notice that
Then we can see that
#coshx/sinhx = cothx = ((e^x + e^(-x))/2)/((e^x - e^(-x))/2) = (e^x + e^(-x))/(e^x - e^(-x))#
Therefore, all we must do is differentiate
Recall that
You can then recall that
Hopefully this helps!
Here's how you would answer by the quotient rule:
#y' = ((e^x - e^(-x))(e^x - e^-x) - (e^x + e^-x)(e^x + e^-x))/(e^x -e^-x)^2#
#y' = (e^(2x) - 2e^(-x)e^x + e^(-2x) - (e^(2x) + 2e^(-x)e^x + e^(-2x)))/(e^x - e^-x)^2#
#y' = (4/e^x e^x)/(e^x - e^-x)^2#
#y' = 4/(e^x- e^-x)^2#
As we got with the other method.
Hopefully this helps!