Very simple maths problem

[big_white_dog84]

What is the differential of e^(x^2) with respect to x?

Please close as soon as I get the answer.

 

[Royality]

23

 

[Sp!ke]

23

Surely its 42?????

You'll probably get some help if you at least try to answer it yourself......

 

[Barbie]

2x * e^(x^2) i believe.

 

[big_white_dog84]

Right.

I know diff of e^x is e^x

Diff of e^2x is 2 e^2x

I don't know how to deal with the extra squared, although i think i might just need to differentiate the power with respect to x therefore giving an answer of 2xe^(x^2)


EDIT - beaten to my own answer!

 

[//Mike]

2x.e^(x^2)

 

[Royality]

I was joking by the way.

 

[Lagz]

You use differentiation by parts:

df/dx = df/dt * dt/dx

let t = x^2 and you get:

f = e^t
df/dt = e^t = e^(x^2)

t = x^2
dt/dx = 2x

df/dx = 2xe^(x^2)

 

[Paulj]

The basic rule is to differentiate the power and bring it to the front works a treat on those questions, its also useful to have memorised examples

 

[Amleto]

You use differentiation by parts:

...

That's called the chain rule isn't it?


for the op:


I always remember:
d/dx[exp(f(x))] = f'(x)exp(f(x))
which is just the chain rule for this specific case.

You may want to keep in mind:
int( f'(x)/f(x) ) dx = int 1/f(x) df = ln (f(x))
for future needs

 

[spirit]

chain rule.. Amleto is correct, but i didnt read Lagz! (i was unaware of diff by parts, theres int by parts, what you are doing Lagz is some kind of subsitution but perhaps im wrong.)

 

[woodsy2k]

Yes, the differential of e^(x^2) is indeed 2x.e^(x^2). Lagz, your correct, you just gave the method the wrong name

The method is the chain rule. The only "by parts" method i know is integration by parts.

It all depends of course how you are taught. Some call it one thing, others call it something else, as long as the method is the same.

 

[Lagz]

Oops yeah its called the chain rule . You forget the names for these things when you first saw them a long time ago!