💬 👋 We’re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here!
Get the answer to your homework problem.
Try Numerade Free for 7 Days
Like
Report
Prove that $ \frac {d}{dx}$ (cot $ x $) = $ - csc^2 x. $
$\frac{d}{d x}(\cot x)=\frac{d}{d x}\left(\frac{\cos x}{\sin x}\right)=\frac{(\sin x)(-\sin x)-(\cos x)(\cos x)}{\sin ^{2} x}=-\frac{\sin ^{2} x+\cos ^{2} x}{\sin ^{2} x}=-\frac{1}{\sin ^{2} x}=-\csc ^{2} x$
00:41
Frank L.
Calculus 1 / AB
Chapter 3
Differentiation Rules
Section 3
Derivatives of Trigonometric Functions
Derivatives
Differentiation
University of Michigan - Ann Arbor
University of Nottingham
Boston College
Lectures
03:09
In mathematics, precalculu…
31:55
In mathematics, a function…
01:20
Prove that $ \frac {d}{dx}…
01:37
03:18
Integrals of cot $x$ and $…
02:24
Prove the formula for $ (d…
01:41
00:39
Proof Prove that $$\in…
02:13
Prove or disprove the iden…
01:01
Verify the formulas by dif…
00:40
Integrals of $\cot x$ and …
02:30
Derive the formula for the…
he It's clear, so enumerated here. So we're gonna do a proof We're gonna start off with our code tangent. So de over de ex coat engine of hacks. Another way to right. This is D over D x of co sign over sign, which is equal to sign when we apply the quotient. Cool de over de ex co sign minus co sign D over the access sign well over sign square. This becomes equal to sign times Negative sign dryness Co sign turns co signed over signed square, which is equal to negative Signed Square Plus Co signed square over a sign square. This becomes equal to negative one for trig identities over sign at square, which is equal to negative co Sika Square.
Campbell University
Oregon State University
Harvey Mudd College
Baylor University
In mathematics, precalculus is the study of functions (as opposed to calculu…
In mathematics, a function (or map) f from a set X to a set Y is a rule whic…
Prove that $ \frac {d}{dx}$ (csc $ x $ ) = - csc $ x $ cot $ x. $
Prove that $ \frac {d}{dx}$ (csc $ x $ ) = sec $ x $ tan $ x. $
Integrals of cot $x$ and $\csc x$Prove that $\int \csc x \, d x=-\ln |\c…
Prove the formula for $ (d/dx) (\cos^{-1} x) $ by the same method as for $ (…
Integrals of cot $x$ and $\csc x$Use a change of variables to prove that…
Proof Prove that $$\int \cot u d u=\ln |\sin u|+C.$$
Prove or disprove the identity.$$\frac{\tan x}{\sec x} \sin (-x)=\cos ^{…
Verify the formulas by differentiation.$$\int \frac{d x}{\sqrt{a^{2}-x^{…
Integrals of $\cot x$ and $\csc x.$Use a change of variables to prove th…
Derive the formula for the derivative with respect to $x$ ofa. $\sec x$<…
