MYTUTOR SUBJECT ANSWERS

816 views

How do I differentiate y = ln(sin(3x))?

So we initially have the relationship y = ln(sin(3x)). As the left hand side is a function of the variable y and the right hand side is a function of the variable x i.e they are implicitly related, we need to use implicit differentiation. This means we differentiate each side of the equation seperately with respect to the functional variable, in this case x. Now differentiate the LHS, which is simple enough

d/dx(y) = dy/dx = f'(x)

To differentiate the RHS, we note that the differential of a logarithm ln(g(x)) is given by g'(x) / g(x), a relationship that can be found easily by integrating. So in this example we have that g(x) = sin(3x), therefore we need to use the chain rule to differentiate it. The differential of sin(3x) is thus cos(3x) multiplied by the differential of 3x which is 3, therefore g'(x) = 3cos(3x)  and so the differential of the RHS is 3cos(3x)/sin(3x) = 3cot(3x)

We thus have dy/dx = 3cot(3x)

Ifan W. GCSE Maths tutor, A Level Maths tutor, A Level Further Mathem...

2 years ago

Answered by Ifan, an A Level Maths tutor with MyTutor


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

179 SUBJECT SPECIALISTS

£20 /hr

Anezka E.

Degree: Mathematics (Bachelors) - Kings, London University

Subjects offered: Maths

Maths

“About me: I'm hopefully about to start my second year at King's College London. I've thouroughly enjoyed studying maths for many years now and would love to help out a maths lover or hater and hopefully convert the latter into the for...”

MyTutor guarantee

£20 /hr

William D.

Degree: Mechanical Engineering (Masters) - Leeds University

Subjects offered: Maths, Physics+ 2 more

Maths
Physics
Italian
Chemistry

“I am a British student currently in the first year of a masters degree in Mechanical Engineering at the University of Leeds. Having previously lived in Spain and Italy, I am fluent in both languages and have excellent communications s...”

£20 /hr

Joel B.

Degree: Mathematics & Computer Science (Bachelors) - Manchester University

Subjects offered: Maths, Physics+ 3 more

Maths
Physics
Further Mathematics
Computing
Chemistry

“About Me: Hello, my name is Joel and I am currently a student at the University of Manchester studying for a joint honours in Mathematics & Computer Science. I have experience in teaching maths (and further maths) to students in the ag...”

MyTutor guarantee

About the author

Ifan W.

Currently unavailable:

Degree: Physics with Theoretical Physics (Masters) - Imperial College London University

Subjects offered: Maths, Physics+ 1 more

Maths
Physics
Further Mathematics

“An Imperial College MSci Physics with Theoretical Physics graduate, 1st class honours. Experienced in tutoring A-Level & GCSE level maths/physics.”

MyTutor guarantee

You may also like...

Posts by Ifan

A note was played on a a keyboard. The frequency of the note was 440 Hz. (a) What does a frequency of 440 Hz mean? (b) The sound waves produced by the keyboard travel at a speed of 340 m/s. Calculate the wavelength of the note.

Find the complex number z such that 5iz+3z* +16 = 8i. Give your answer in the form a + bi, where a and b are real numbers.

How do I differentiate y = ln(sin(3x))?

Other A Level Maths questions

What is the difference between a scalar and vector quantity?

What is trigonometry? How do I remember sine, cosine and tangent?

How would you differentiate f(x) = 2x(3x - 1)^2 using the chain rule?

Differentiate y=x*ln(x^3-5)

View A Level Maths tutors

Cookies:

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

mtw:mercury1:status:ok