Originally Posted by
sk8erboyla2004 $\displaystyle \sqrt{z} * e^{-z}$
find derivative
this is the answer i came up with
$\displaystyle \frac{1}{2\sqrt{z}}e^{-z}+\sqrt{z}e^{-z}$
however the solution the manual was rather subtraction instead of addition ? the reason the book answer was subtraction, is because they moved the $\displaystyle e^{-z}$ to the denominator and turned it into $\displaystyle \frac{\sqrt{z}}{e^z}$ & used the quotient rule.
so you would have:
$\displaystyle \frac{\sqrt{z}}{e^z}$
$\displaystyle = \frac{z^{\frac{1}{2}}e^z - \frac{1}{2}z^{-\frac{1}{2}}e^z}{e^{2z}}$
also
$\displaystyle \sqrt{(x^{2}*5^{x})^{3}}$
urgent response needed
find the derivative
i got this not really simplified and im not sure how to
$\displaystyle \frac{3}{2}\sqrt{(x^{2}*5^{x})}[5^{x}(2x+x^{2}(ln5)]$