Derivate f(x)=x^2*e*(-3x)

**Blacklaw** · January 6th 2010, 03:57 AM

Hi guys

I've been trying to solve this for a little while now but I feel kinda lost and I thought you could maybe help me out.

so

f(x)=x^2*e^(-3x)

f '(x)=?

Thank you.

**dedust** · January 6th 2010, 04:01 AM

Originally Posted by Blacklaw

Hi guys

I've been trying to solve this for a little while now but I feel kinda lost and I thought you could maybe help me out.

so

f(x)=x^2*e^(-3x)

f '(x)=?

Thank you.

$<br /> f(x) = g(x)h(x)$ , then $f'(x) = g'(x)h(x) + g(x)h'(x)$

take $g(x) = x^2$ and $h(x) = e^{-3x}$

**Blacklaw** · January 6th 2010, 04:12 AM

Originally Posted by dedust

$<br /> f(x) = g(x)h(x)$ , then $f'(x) = g'(x)h(x) + g(x)h'(x)$

take $g(x) = x^2$ and $h(x) = e^{-3x}$

I get $2x*e^{-3x}+x^2*e^{-3x}$

But I know for a fact that the correct answer is $2x*e^{-3x}+x^2*e^{-3x}*(-3)$

Please explain how I get the (-3)?

**CaptainBlack** · January 6th 2010, 04:16 AM

Originally Posted by Blacklaw

I get $2x*e^{-3x}+x^2*e^{-3x}$

But I know for a fact that the correct answer is $2x*e^{-3x}+x^2*e^{-3x}*(-3)$

Please explain how I get the (-3)?

$\frac{d}{dx}e^{-3x}=-3e^{-3x}$

You did not know the answer for a fact if it was what was in the back of the book. You know it for a fact if you know why it is so and now you should do.

CB

**Blacklaw** · January 6th 2010, 04:31 AM

Originally Posted by CaptainBlack

$\frac{d}{dx}e^{-3x}=-3e^{-3x}$

You did not know the answer for a fact if it was what was in the back of the book. You know it for a fact if you know why it is so and now you should do.

CB

Does it always go like that? I thought the derivative of $e^x$ was $e^x$ ?

Thank you for you help, I truly appreciate it.

**tom@ballooncalculus** · January 6th 2010, 05:24 AM

Originally Posted by Blacklaw

Does it always go like that?

That's what the chain rule says.

Just in case a picture helps...

is the chain rule. Straight continuous lines differentiate downwards (integrate up) with respect to x, and the straight dashed line similarly but with respect to the dashed balloon expression (the inner function of the composite which is subject to the chain rule).

In this case...

PS:

Just in case another picture doesn't hurt (and in view of comments below)...

Wrapping the chain rule inside the (legs-uncrossed version of) ...

... the product rule, we get...

__________________________________________
Don't integrate - balloontegrate!

Balloon Calculus; standard integrals, derivatives and methods

Balloon Calculus Drawing with LaTeX and Asymptote!

**Blacklaw** · January 6th 2010, 05:34 AM

I think I get it now.. Thank you very much for helping me out.

**rshekhar.in** · January 6th 2010, 09:13 AM

$f(x) = x^2 e^{-3x}$
$f'(x) = x^2 e^{-3x} (-3) + e^{-3x} 2x$ By chain rule
$f'(x) = x e^{-3x} [ -3x + 2 ]$

Hope this helps.

**CaptainBlack** · January 6th 2010, 09:23 AM

Originally Posted by rshekhar.in

$f(x) = x^2 e^{-3x}$
$f'(x) = x^2 e^{-3x} (-3) + e^{-3x} 2x$ By chain rule
$f'(x) = x e^{-3x} [ -3x + 2 ]$

Hope this helps.

What you label as "by chain riue" is mainly product rule and to a lesser extent chain rule

CB

**CaptainBlack** · January 6th 2010, 09:26 AM

Originally Posted by Blacklaw

Does it always go like that? I thought the derivative of $e^x$ was $e^x$ ?

Thank you for you help, I truly appreciate it.

The derivative of $e^x$ is $e^x$ but that is not what you have, what you should know is that the derivative of $e^{ax}$ is $ae^{ax}$ by the chain rule if you must, but you should know it because it will occur so often.

CB

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