Differentiate y=x/sin(x)

This equation has one function of x divided by another function of x, we therefore have to use the quotient rule and is written in the form f(x)/g(x). 

The quotient rule is therefore

f'(x)g(x)-g'(x)f(x)/g2(x)

The first step would be to differentiate f(x) and g(x). 

f'(x)=1 g'(x)=cos(x)

The numerator of this fraction would therefore be 

1*sin(x)-xcos(x) =sin(x)-xcos(x)

To calculate the denominator you simply square g(x)

g2(x)= sin2(x)

So the answer would be sin(x)-xcos(x)/sin2(x)

Answered by Rowan F. Maths tutor

23645 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

How do I differentiate implicitly?


A curve has equation -2x^3 - x^2 + 20x . The curve has a stationary point at the point M where x = −2. Find the x-coordinate of the other stationary point of the curve.


What is implicit differentiation and how do I do it?


Solve the following simultaneous equations: 3x + 5y = -4 and -2x + 3y = 9


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences