derivative of e

[shizzy]

Can someone explain to me why the following is true:

f(x) = e^6x
f'(x) = 1/6*e^6x

 

[Matt]

What you wrote is false. Actually, f'(x) = 6*e^(6x)

 

[shizzy]

sorry. Think I figured it out. Think what that is, is the integration of f(x) not the derivative. Was reading the little refresher tutorial wrong. So...

If f(x) = e^6x
f'(x) = 6e^6x

and if f(x) = e^6x
then the indefinate integral is: 1/6*e^6x

can you guys tell me if I'm on the right track here or not? Taking calc4 this fall after not being in math for a year so I'm trying to get myself caught back up. Thanks!

 

[shizzy]

thanks matt! Man you replied really fast!

 

[tkhunny]

and if f(x) = e^6x
then the indefinate integral is: 1/6*e^6x

Right track? It appears so. At the station? Not quite.

I don't know if your refresher mentions the Constant of Integration. It should.

Find the derivative of these four functions:

f(x) = e^(x)
g(x) = e^(x) + 6
h(x) = e^(x) - 3
k(x) = e^(x) + 256

Now, tell me what is THE antiderivative of:

m(x) = e^(x)

 

[shizzy]

Haha. Okay, yeah you got me! That sneaky little constant of integration keeps tricking me but I'm finally starting to get it down. THE correct answer should be:

f(x) = e^(x) + C

thanks again!!

 

[tkhunny]

There is still a little notation problem.

You have f(x) = e^6*x.

Normally, it would be considered bad form to give the antideriviative the same name. A common convention is to use upper case for the antiderivative.

F(x) = (1/6)*e^6*x + C

Good work. I think you have it.