Question

Differentiate the function.

Answer 1

can't load it

Answer 2

lol.

Answer 3

Yeah, I'm afraid I can't open that .cgi file either. What does it come from?

Answer 4

h(z)=\[\ln(\sqrt{(7-z^2)/(7+z^2})\]

Answer 5

\[1/\sqrt{(7-z^2)/(7+z^2)}\] i believe that is how you differentiate a natural log.

Answer 6

i have to have the derivative of the inside of the natural log

Answer 7

oh yes. sorry. \[(1/2)((7-z^2)/(7+z^2))^{-1/2}*(((7+z^2)(-2z)-(7-z^2)(2z))/(7+z^2)^2)\] looks better on paper

Answer 8

if you want i can put that on paper and attach a photo

Answer 9

Why not expand the natural log first so you don't have such a messy chain rule...
\[ y=\ln \sqrt{ \frac{7-x^2}{7+x^2}} \]
\[y=\frac{1}{2} \ln\frac{7-x^2}{7+x^2}\]
\[y=\frac{1}{2} \ln(7-x^2) - \frac{1}{2} \ln(7+x^2) \]
So the derivative is a simpler chain rule
\[y' = \frac{1}{2} \cdot\frac{-2x}{7-x^2} - \frac{1}{2} \cdot \frac{2x}{7+x^2} \]
\[y' = \frac{-x}{7-x^2} - \frac{x}{7+x^2} \]