# Finding derivative of sin^-1 (x^2 + 1)

1. Apr 17, 2010

### thereddevils

1. The problem statement, all variables and given/known data

Diffentiate $$f(x)=\sin^{-1}(x^2+1)$$

2. Relevant equations

3. The attempt at a solution

$$f'(x)=(-1)(2x)\sin^{-2} (x^2+1)\cos (x^2+1)$$

am i correct ? But wolfram alpha is giving me something else

http://www.wolframalpha.com/input/?i=differentiate+sin^(-1)+(x^2+1)

2. Apr 17, 2010

### tiny-tim

Hi thereddevils!

(try using the X2 tag just above the Reply box )

you've correctly differentiated f(x) = 1/sin(x2+1) ,

but the question means f(x) = arcsin(x2+1)

(see eg http://mathworld.wolfram.com/InverseTrigonometricFunctions.html" [Broken] doesn't help at all )

Last edited by a moderator: May 4, 2017
3. Apr 17, 2010

### thereddevils

Re: differentiation

thanks tiny , but whats that tag for ? seems that it makes my font smaller .

4. Apr 17, 2010

### tiny-tim

Should be smaller, but higher up: 222 … wheee! :tongue2:

Are you using the same tag as me? …

it's on the second row (the one that starts B I U …), six from the end

5. Apr 17, 2010

### thereddevils

Re: differentiation

x2 , wow never know it can be done that way , interesting !!

Vo

Why is there no latex tags in this forum ? I will need to type the tags myself which is sometimes troublesome

6. Apr 17, 2010

### tiny-tim

The ∑ tag (at the end of the line) gives you lots of latex symbols, and the first one you click also gives you [noparse]$$and$$[/noparse]

7. Apr 19, 2010

### ammontgo

Re: differentiation

Table of Derivatives:
[PLAIN]https://dl.dropbox.com/u/4645835/MATH/derv_arcsin.gif [Broken]

Last edited by a moderator: May 4, 2017
8. Apr 19, 2010

### Susanne217

Re: differentiation

Remember the Chain rule, reddevils?

which says let

y = y(u(x)) where derivative is

$$\frac{dy}{dx} = \frac{dy}{du} \cdot \frac{du}{dx}$$

which you properly also know as

$$(f \circ g)'(x) = f'(g(x)) \cdot g'(x)$$

since you know that

$$f(u) = sin^{-1}(u)$$

and

$$u = x^2+1$$

then its up to you to use formula above correctly :D

Sincerely
Susanne

9. Apr 20, 2010

### thereddevils

Re: differentiation

thanks Susan .

10. Apr 21, 2010

### Susanne217

Re: differentiation

You are welcome!