How do you find the derivative of $y=(e^x+e^-x)/4$ ?

Question

1720 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-05-24T14:05:27

$dy/dx = (e^x-e^(-x))/4 = 1/2sinhx$

We have:

$y = (e^x+e^(-x))/4$

Differentiating directly:

$dy/dx = (e^x-e^(-x))/4$

Also, If you are familiar with the hyperbolic functions then we can proceed as follows:

$y = (e^x+e^(-x))/4$

$\ \ = 1/2 * (e^x+e^(-x))/2$

$\ \ = 1/2coshx$

and so:

$dy/dx = 1/2sinhx$

How do you find the derivative of y=(e^x+e^-x)/4y=(e^x+e^-x)/4?