prove-that-frac-ddx-csc-x-csc-x-cot-x

Name: prove that frac ddx csc x csc x cot x
Uploaded: 2019-12-09
Duration: 1 min 20 s
Channel: Numerade
Description: Prove that $ \frac {d}{dx}$ (csc $ x $ ) = - csc $ x $ cot $ x. $

Question

Prove that $ \frac {d}{dx}$ (csc $ x $ ) = - csc $ x $ cot $ x. $

Clarissa Noh · Accepted Answer

Hey, it&#x27;s clear. So when you reign here, So our first steps gonna be taking the derivative of coast seeking, which is one over sign and we&#x27;re gonna use the quotient role, Which gives us sign times zero minus one times co sign all over Sign square. This gives us negative co sign over a sign square, and this is negative. One over. Sign Times Co sign over a sign which gives us negative co secret tons co tangent.

Problem

Prove that $ \frac {d}{dx}$ (csc $ x $ ) = sec $ …

Problem 17 Easy Difficulty

Prove that $ \frac {d}{dx}$ (csc $ x $ ) = - csc $ x $ cot $ x. $

Answer

$\frac{d}{d x}(\csc x)=\frac{d}{d x}\left(\frac{1}{\sin x}\right)=\frac{(\sin x)(0)-1(\cos x)}{\sin ^{2} x}=\frac{-\cos x}{\sin ^{2} x}=-\frac{1}{\sin x} \cdot \frac{\cos x}{\sin x}=-\csc x \cot x$

More Answers

Related Courses

Calculus: Early Transcendentals

Related Topics

Discussion

Top Calculus 1 / AB Educators

Catherine R.

Caleb E.

Kristen K.

Samuel H.

Calculus 1 / AB Courses

Precalculus Review - Intro

Functions on the Real Line - Overview

Recommended Videos

Watch More Solved Questions in Chapter 3

Video Transcript