# How do you differentiate #y=e^(e^x)#?

##### 1 Answer

#### Explanation:

If you are studying maths, then you should learn the Chain Rule for Differentiation, and practice how to use it:

If

# y=f(x) # then# f'(x)=dy/dx=dy/(du)(du)/dx #

I was taught to remember that the differential can be treated like a fraction and that the "

# dy/dx = dy/(dv)(dv)/(du)(du)/dx # etc, or# (dy/dx = dy/color(red)cancel(dv)color(red)cancel(dv)/color(blue)cancel(du)color(blue)cancel(du)/dx) #

So we have

Using

# dy/dx=(e^u)(e^x) #

# :. dy/dx=(e^(e^x))(e^x) #

# :. dy/dx=e^(x+e^x) #