# Can someone check my answer please?

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• Aug 5th 2009, 08:44 AM
Darkhrse99
Can someone check my answer please?
Take the derivative of \$\displaystyle 5x^2e^3x\$

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

Thanks
• Aug 5th 2009, 08:49 AM
e^(i*pi)
Quote:

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

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

Thanks

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

Using the product rule

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

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

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

\$\displaystyle f'(x) = 10xe^{3x} + 15x^3e^{3x} = 5xe^{3x}(2+3x^2)\$
• Aug 5th 2009, 08:49 AM
Plato
Quote:

Originally Posted by Darkhrse99
Take the derivative of \$\displaystyle 5x^2e^3x\$
I got \$\displaystyle 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.
[tex]x^{3x}[/tex] gives \$\displaystyle x^{3x} \$ instead of \$\displaystyle x^3x\$.