# Product rule

• February 12th 2009, 05:30 PM
TastyBeverage
Product rule
Starting with x^(1/2) * e^x

i have gotten to g(x) = x^(1/2)(e^x) + e^x(1/2x^(-1/2))

what would be the next algebraic (sp) step?
• February 12th 2009, 05:59 PM
wytiaz
factor out e^x, perhaps also factor out x^(-1/2)
• February 12th 2009, 08:37 PM
mollymcf2009
Quote:

Originally Posted by TastyBeverage
Starting with x^(1/2) * e^x

i have gotten to g(x) = x^(1/2)(e^x) + e^x(1/2x^(-1/2))

what would be the next algebraic (sp) step?

You could also move the $x^{-\frac{1}{2}}$ to the denominator as $\sqrt x$

$\frac{e^x}{2\sqrt x} + e^x\sqrt x$

I guess if you wanted to do more, you could get a common denominator and combine the two. Not sure how far your teacher wants you to take it.