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


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)

Rowan F. A Level Chemistry tutor, GCSE Biology tutor, GCSE Chemistry ...

1 year ago

Answered by Rowan, an A Level Maths tutor with MyTutor

Still stuck? Get one-to-one help from a personally interviewed subject specialist


£20 /hr

Vinay S.

Degree: Aerospace Engineering (Masters) - Bath University

Subjects offered:Maths, Science+ 4 more

Further Mathematics
-Personal Statements-

“About Me: Hey! I'm a Aerospace Engineering student at the University of Bath. Although my course suggests I'm simply a Maths and Physics kind of guy, I also have a huge passion for Economics, so please feel free to pick my brain on any...”

MyTutor guarantee

PremiumFerdinand B. A Level Biology tutor, A Level Chemistry tutor, GCSE Che...
£30 /hr

Ferdinand B.

Degree: Medical Sciences (Bachelors) - Exeter University

Subjects offered:Maths, French+ 2 more


“​About me: I'm currently studying Medical Sciences at the University of Exeter. I love this course as it doesn't only incorporate the key biological concepts, but also focuses on the medical application of these. ​I've always had a hu...”

£20 /hr

Andrew G.

Degree: Physics (Bachelors) - Exeter University

Subjects offered:Maths, Physics


“About Me: I am Physics student studying at University of Exeter. I have a real passion for my subject and would love the opportunity to pass on some of my knowledge and experiences. As well as making tough subjects fun and easy to und...”

MyTutor guarantee

About the author

£22 /hr

Rowan F.

Degree: Chemistry (Masters) - Bristol University

Subjects offered:Maths, Chemistry+ 1 more


“About Me  I am a first year Chemistry student at the University of Bristol and a long with my love for Chemistry I am also incredibly interested in Maths and Biology, enjoying studying both of them at A level. By tutoring that I hope ...”

You may also like...

Posts by Rowan

Differentiate y=x/sin(x)

How will the position of equilibrium shift for an endothermic reaction when heated?

What causes bacteria to become antibiotic resistant?

Other A Level Maths questions

Sketch the graph y=Ax^2 where A is a constant

What is the dot product of two vectors?

Find the integral of xe^(-2x) between the limits of 0 and 1 with respect to x.

How do you go about differentiating a^x functions?

View A Level Maths tutors

We use cookies to improve your site experience. By continuing to use this website, we'll assume that you're OK with this. Dismiss