Differentiate cosecx

• Jun 13th 2006, 12:38 AM
nath_quam
Differentiate cosecx
Prove that d/dx (cosecx) = -cosecxcotx
• Jun 13th 2006, 04:53 AM
topsquark
Quote:

Originally Posted by nath_quam
Prove that d/dx (cosecx) = -cosecxcotx

cscx = 1/sinx

-Dan
• Jun 13th 2006, 05:13 AM
CaptainBlack
What would you like us to do with the attachment?

RonL
• Jun 13th 2006, 06:13 AM
Jameson
For part (a) integrate dI and then using your initial value solve for the constant of integration.
• Jun 13th 2006, 11:47 AM
ThePerfectHacker
Since,
$\csc x=\frac{1}{\sin x}$
Then, when you take its derivative apply quotient rule,
$(\csc x)'=\frac{(1)'\sin x+1(\sin x)'}{\sin^2 x}$
Then,
$(\csc x)'=\frac{0\cdot \sin x-1\cdot \cos x}{\sin^2 x}=\frac{-\cos x}{\sin ^2x}$= $\frac{-\cos x}{\sin x}\cdot \frac{1}{\sin x}=-\cot x\sin x$
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For reference,
If $f(x)$ is a diffrenciable function at $x=c$ and $g(x)$ is a diffrenciable function at $x=c$ such as, $g(c)\not = 0$, then $f(x)/g(x)$ is diffrenciable at $x=c$ and its derivative at $x=c$is,
$\frac{f'(c)g(c)-f(c)g'(c)}{[g(c)]^2}$
• Jun 13th 2006, 02:29 PM
nath_quam
Quotient Rule
Perfect Hacker shouldn't the quotient rule have a minus in the middle not a plus as you have it Thanks Nath and how would i go about doing the three parts of the attachment
• Jun 13th 2006, 02:53 PM
ThePerfectHacker
Quote:

Originally Posted by nath_quam
not a plus as you have it

A plus!
Where do you see a plus?

(Okay I admit I edited my message, you are right)