# Differentiation

• Mar 6th 2009, 01:25 AM
katieeej
Differentiation
The problem is to determine where the function is increasing, decreasing, concave up and concave down.

1) y=(2x-3)^(1/3)

2) y=1/(1+e^-x)

for the first one, i got the first derivative of (1) 2/3(2x-3)^(-2/3)
but im not sure if this is right.
and i have no idea for the second derivative.
and i really really have no idea for the second problem.
• Mar 6th 2009, 03:13 AM
thelostchild

for the second just differentiate your expression for the first derivative again, you used the chain rule for the first I'm guessing so just use it again.

I get

$
\frac{d^2y}{dx^2}=-\frac{8}{9}(2x-3)^{-\frac{5}{3}}
$

For the second one rewrite it as

$
y=(1+e^{-x})^{-1}
$

then use the chain rule

I get $\frac{e^{-x}}{(1+e^{-x})^2}$

Then use the quotient rule on this to get the second derivative