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) #