Question

differentiate
sin((1+x2)/(1-x2)),
My question is that is a possible substitution possible ???

Answer 1

differentiate means? find derivative?

Answer 2

yes

Answer 3

yes...find d/dx of the function given...

Answer 4

chain and quotient/product

Answer 5

\[\frac{\sin(1+x^2)}{1-x^2}\]?
and why do you want to substitute?

Answer 6

i think the sin has the fraction as the argument :)

Answer 7

its chain rule,

\[\frac{dy}{dx} = \frac{dy}{du} \frac{du}{dx}\]

Answer 8

\[\sin ((1+x2)\div(1-x2))\]

Answer 9

so let u = (1+x^2)/(1-x^2)

so y = sinu

now find dy/du

and du/dx

and multiply to get dy/dx

Answer 10

i know how to diferentiate it using quotient rule etc..but can i substitute any other function in place of x to make it simpler???

Answer 11

@amistre64 - is it possible to substitute any other function in place of x to make it simpler???

Answer 12

we dont tend to substiture for differentiation really, its integration where that comes in handy

i mean substituting another function for x.. would it really be worth it? i cant see how it would make it simpler than just quotient ruling it, but if you have a substitution that does
please share, i could be wrong

Answer 13

x(x) is already a pretty simple function in its own right

Answer 14

x=trig might produce something different tho ... not sure how simple it would make it tho

Answer 15

suppose in this Q
sin(inv)((1-x)/(1+x))
here we sub using cos2x...
a similar sub i am asking for...

Answer 16

x = cos2x is not a substitution .... x = cos(2t) might be

Answer 17

ohh

Answer 18

mistype