# Thread: product rule derivative check!

1. ## product rule derivative check!

$\displaystyle y = x^2cscx\sqrt{x^2+1}$

its derivative is :

$\displaystyle y' = 2xcscx\sqrt{x^2+1} - x^2cotxcscx\sqrt{x^2+1} + x^2cscx\frac{1}{2\sqrt{x^2+1}}$

correct?

2. Not quite

$\displaystyle y' = 2xcscx\sqrt{x^2+1} - \bigg(x^2cotxcscx\sqrt{x^2+1}\bigg)\bigg(\frac{2x} {2\sqrt{x^2+1}}\bigg)$

Oops nevermind didn't see that there was an x behinf the csc

3. Originally Posted by 11rdc11
Not quite

$\displaystyle y' = 2xcscx\sqrt{x^2+1} - \bigg(x^2cotxcscx\sqrt{x^2+1}\bigg)\bigg(\frac{2x} {2\sqrt{x^2+1}}\bigg)$
hrmm what happened to the $\displaystyle + x^2cscx$ ? and the 2x where it come from? thank u

4. Originally Posted by 11rdc11
Not quite

$\displaystyle y' = 2xcscx\sqrt{x^2+1} - \bigg(x^2cotxcscx\sqrt{x^2+1}\bigg)\bigg(\frac{2x} {2\sqrt{x^2+1}}\bigg)$

Oops nevermind didn't see that there was an x behinf the csc
so is mine okay ?

5. $\displaystyle$
$\displaystyle y' = 2xcscx\sqrt{x^2+1} - (x^2cotxcscx\sqrt{x^2+1}) + x^2cscx\frac{2x}{2\sqrt{x^2+1}}$
$\displaystyle$

6. Quick question is it

$\displaystyle x^2csc(x\sqrt{x^2 -1})$

or

$\displaystyle x^2(cscx)(\sqrt{x^2-1})$

7. Originally Posted by jvignacio
so is mine okay ?
$\displaystyle y' = 2xcscx\sqrt{x^2+1} - (x^2cotxcscx\sqrt{x^2+1}) + x^2cscx\frac{x}{\sqrt{x^2+1}}$

8. Originally Posted by 11rdc11
Quick question is it

$\displaystyle x^2csc(x\sqrt{x^2 -1})$

or

$\displaystyle x^2(cscx)(\sqrt{x^2-1})$
its the 2nd one

9. Originally Posted by jvignacio
$\displaystyle y' = 2xcscx\sqrt{x^2+1} - (x^2cotxcscx\sqrt{x^2+1}) + x^2cscx\frac{x}{\sqrt{x^2+1}}$