Math Help - Derivitive with the power rule

1. Derivitive with the power rule

Can any one help me solve d/dx $e^(3x^2+8x)$

my answer of $e^(3x^2+8x)(6x+8)(3x^2+8x)+e^(3x^2+8x)(6x+8)$ is not correct.

2. Hello,
Originally Posted by skyslimit
Can any one help me solve d/dx $e^(3x^2+8x)$

my answer of $e^(3x^2+8x)(6x+8)(3x^2+8x)+e^(3x^2+8x)(6x+8)$ is not correct.
Let $u(x)=3x^2+8x$

So you have to find the derivative of $e^{u(x)}$

Chain rule says : $\Bigg([f(g(x))]'=g'(x)f'(g(x))$. Here, $g(x)=u(x)$ and $f(t)=e^t \Bigg)$ -additional part-

Hence we have that the derivative of $e^{u(x)}$ is $u'(x)e^{u(x)}$

Substitute $u(x)$ and $u'(x)$

3. Thanks, thatd worked. Now For more complicated ones $(x-3)^9e^x$

I get $(x-3)^8[9(e^x)+(x-3)(e^x)]$, but that is still not correct. Any suggestions?

4. Originally Posted by skyslimit
Thanks, thatd worked. Now For more complicated ones $(x-3)^9e^x$

I get $(x-3)^8[9(e^x)+(x-3)(e^x)]$, but that is still not correct. Any suggestions?
Hmmm well this is correct o.O
But the completely factorised form is :

$(x-3)^8 e^x [9+(x-3)]=(x-3)^8 e^x [x+6]$

5. Thanks again )