Differentiate the function: y = sin(x^2)*ln(5x)

We are tasked with differentiating y = sin(x2)*ln(5x)

This function is actually a product of the functions:

sin(x2) and ln(5x)

Therefore the product rule will be required.

First let's calculate the derivatives of our individual functions before combining them.

The derivative of sin(x2) is 2x*cos(x2) using the chain rule.

The derivative of ln(5x) is 1/x.

Now to combine these using the product rule. Our answer will be:

2x*cos(x2)*ln(5x) + sin(x2)*1/x

Thomas C. 11 Plus Maths tutor, A Level Maths tutor, 13 plus  Maths tu...

5 months ago

Answered by Thomas, an A Level Maths tutor with MyTutor

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


£24 /hr

Daniel R.

Degree: Mathematics (Bachelors) - Durham University

Subjects offered: Maths, Physics+ 1 more

Further Mathematics

“About me I’m a first year student studying Maths with European Studies at Durham. I have recently taken my A levels, achieving A* in Maths and Further Maths, so I am familiar with the course content and what the examiners are looking ...”

£20 /hr

Liberty A.

Degree: Mathematics (Bachelors) - Durham University

Subjects offered: Maths, Physics+ 1 more

Further Mathematics

“About Me Hi I'm Libby, I am in my first year studying Mathematics at Durham University and live in Buckinghamshire. I believe Mathematics and Pysics are fantastic subjects and I enjoy tutoring as I am able to share my passion and help...”

MyTutor guarantee

£24 /hr

Hinsum W.

Degree: Medicine (Bachelors) - Edinburgh University

Subjects offered: Maths, Chemistry+ 3 more

-Personal Statements-
-Medical School Preparation-

“Hi, I'm a first year medic at Edinburgh. I've had 7 years' worth of experience teaching children Maths and English and have mentored lower school peers, so I'm bound to have an approach that will suit your learning style!”

About the author

Thomas C.

Currently unavailable: for new students

Degree: Natural Sciences (Physical) (Bachelors) - Cambridge University

Subjects offered: Maths, Science+ 7 more

Further Mathematics
-Personal Statements-
-Oxbridge Preparation-

“Hi! I`m Tom, a 2nd year Natural Sciences undergraduate at Cambridge University. I am a very positive and empathetic person with a love for the Sciences. I am an experienced tutor in Maths, Physics and Chemistry from GCSE to A level a...”

You may also like...

Posts by Thomas

A 0.20 kg mass is whirled round in a vertical circle on the end of a light string of length 0.90 m. At the top point of the circle the speed of the mass is 8.2 m/s. What is the tension in the string at this point?

Differentiate the function: y = sin(x^2)*ln(5x)

How many moles of Magnesium must react with excess Oxygen to produce 80g of Magnesium oxide?

If a cricket ball of mass 500g is thrown upwards from the ground with an initial velocity of 20 m/s, how high will the ball reach?

Other A Level Maths questions

Given df/dx=2x+3 and the graph goes through (1,1), what is the function f?

Solve the equation d/dx((x^3 + 3x^2)ln(x)) = 2x^2 + 5x, leaving your answer as an exact value of x. [6 marks]

How do I integrate log(x) or ln(x)?

Given that y = exp(2x) * (x^2 +1)^(5/2), what is dy/dx when x is 0?

View A Level Maths tutors


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