Thread: A little stuck on a derivative

1. A little stuck on a derivative

i was trying to differentiate h(x) = (1-x^(2))^(1/2) * arcsin(x^(2))

I came up with (2x^(2))/[((1-x^(2))^(1/2)) * ((1-x^(4))^(1/2))]

can that be simplified further? My algebra is a little rusty... Thanks for your time.

2. Originally Posted by drain
i was trying to differentiate h(x) = (1-x^(2))^(1/2) * arcsin(x^(2))

I came up with (2x^(2))/[((1-x^(2))^(1/2)) * ((1-x^(4))^(1/2))]

can that be simplified further? My algebra is a little rusty... Thanks for your time.
Why is there no arcsin in you derivative?

RonL

3. Hello, drain!

Product rule?

Differentiate: .h(x) .= .(1 - x²)^½ · arcsin(x²)

. . . . . . . . . . . . . . . . . . .2x
h'(x) . = . (1 - x²)^½ · ----------- .+ .½(1 - x²)^{-½)·(-2x) · arcsin(x²)
. . . . . . . . . . . . . . . . √1 - x^4

It doesn't simplify very much . . .
. . . . . . . . . . _____
. . . . . . . .2x√1 - x² . . .x·arcsin(x²)
h'(x) . = . ------------ .- .--------------
. . . . . . . √1 - x^4 . . . . 2√1 - x²

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Hmmm . . .
. . . . . . . . . . . . . . . . . . . . . . . .2x
The first fraction reduces to: . -----------
. . . . . . . . . . . . . . . . . . . . . .√1 + x²

4. Thanks to both of you very much! Guess I still need some practice on these And thanks for the quickmath site! Good way to check my work =)