You are Here: Home >< Maths

# Differentiating e^x^x^x watch

1. This is just for fun...to see if i can do it...

I'm trying to differentiate e^x^x^x

Let y = e^x^x^x

y = [(e^x)^x]^x

THe Chain Rule states dy/dx = dy/du * du/dx

Let u = e^x^x

==> y = u^x

dy/du = xu^(x-1)

du/dx:

u = (e^x)^x

Let a = e^x

Therefore u = a^x

du/dx = xa^x-1

= x(e^x)^x-1

dy/dx = dy/du * du/dx

= xu^(x-1) * x(e^x)^(x-1)

2. you are an odd person. I would do it, but the prospect's highly daunting.
3. Note that the expression e^x^x^x is ambiguous (is it e^(x^x^x) or (e^x^x)^x?) and the convention is to treat it as e^(x^x^x) which is different from what you're doing.

The reason for this convention is that (a^b)^c is just a^(bc). Apply this several times and you'll see ((e^x)^x)^x actually simplifies quite nicely.

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: January 19, 2010
Today on TSR

### Are you living on a tight budget at uni?

From budgets to cutbacks...

### University open days

1. University of Cambridge
Wed, 26 Sep '18
2. Norwich University of the Arts
Fri, 28 Sep '18
3. Edge Hill University
Faculty of Health and Social Care Undergraduate
Sat, 29 Sep '18
Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams