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.
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