Take the derivative of $5x^2e^3x$

I got $10xe^3x(2x+3)$ The X afeter the 3 are suppose to be with the 3 and not lower then the 3.

Thanks

2. Originally Posted by Darkhrse99
Take the derivative of $5x^2e^3x$

I got $10xe^3x(2x+3)$ The X afeter the 3 are suppose to be with the 3 and not lower then the 3.

Thanks
$f(x) = 5x^2e^{3x}$

Using the product rule

$u = 5x^2 \: , \: u' = 10x$

$v = e^{3x} \: , \: v' = 3xe^{3x}$

$f'(x) = u'v + v'u$

$f'(x) = 10xe^{3x} + 15x^3e^{3x} = 5xe^{3x}(2+3x^2)$

3. Originally Posted by Darkhrse99
Take the derivative of $5x^2e^3x$
I got $10xe^3x(2x+3)$ The X afeter the 3 are suppose to be with the 3 and not lower then the 3.
If you have more than one character in an exponent, set off the whole exponent in braces.
$$x^{3x}$$ gives $x^{3x}$ instead of $x^3x$.