Question

derivative of sech^2 (1-x^2)?
is it equal to 4x sech^2 (1-x^2) tanh (1-x^2)??

Answer 1

Let's see, shall we?
You know the chain rule, right?

Answer 2

yeah?

Answer 3

Right, so that
sech^2 (1-x^2), this is just
[sech (1-x^2)]^2
right?

Answer 4

yes

Answer 5

I like to think of chain rule as "dealing with the functions, one by one"
So, make believe for now that that thing that's being squared
\[sech (1-x^{2})\]
is just one big fancy x...
How would you normally differentiate x^2 ?

Answer 6

what i did was:
y=sech^2 (1-x^2)
y'= 2sech(1-x^2) * (-sech(1-x^2))* (tanh(1-x^2))* (-2x)
there....
differentiating x^2 is like:
2 multiply to x then the differentiation of x

Answer 7

Awesome, it looks like you know definitely know what you're doing then :)

Answer 8

thanks :)