MYTUTOR SUBJECT ANSWERS

245 views

If n is an integer such that n>1 and f(x)=(sin(n*x))^n, what is f'(x)?

Let us denote sin(nx) = u(x), where u is a function of x. The equation is now therefore f(x) =(u(x))^n.

For simplicity, we will write that as f(x) = u^n

By the chain rule, we know that f'(x) = df/dx = (df/du)*(du/dx).

Firstly computing df/du, we find df/du = n*u^(n-1)

Now we need to find du/dx. Since u = sin(nx) , du/dx = ncos(nx).

Therefore, our answer is f'(x) = (df/du)*(du/dx) = n*u^(n-1)*ncos(nx), 

subbing in u = sin(nx) yields the final answer:

f'(x) = n(sin(nx))^(n-1)*ncos(nx)

Noam T. A Level Maths tutor, GCSE Maths tutor, A Level Physics tutor,...

6 months ago

Answered by Noam, an A Level Maths tutor with MyTutor


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

264 SUBJECT SPECIALISTS

£22 /hr

Sam F.

Degree: Economics with Placement (Bachelors) - Bath University

Subjects offered:Maths, Physics+ 2 more

Maths
Physics
Extended Project Qualification
Economics

“Studying for BSc Hons Economics, A level economics, maths and physics. Able to tutor GCSE/AS/A2 Economics, Maths and GCSE physics! ”

£20 /hr

Thomas P.

Degree: Computing (Bachelors) - Imperial College London University

Subjects offered:Maths, Physics+ 3 more

Maths
Physics
Further Mathematics
Computing
-Personal Statements-

“Computing student at Imperial College London, particularly enjoying the discreet maths course here. A*A*AA in Maths, Further Maths, Physics and Computing.”

MyTutor guarantee

PremiumGiulio P. GCSE Maths tutor, A Level Maths tutor, A Level Economics tu...
£36 /hr

Giulio P.

Degree: Mathematics (Masters) - Bristol University

Subjects offered:Maths, Physics+ 3 more

Maths
Physics
Italian
Further Mathematics
Economics

“Exam Time! I can provide a rapid revision class in any maths module which will test your son or daughter in all the fundamentals”

About the author

Noam T.

Currently unavailable: for regular students

Degree: Mathematics with Mathematical Physics (Bachelors) - University College London University

Subjects offered:Maths, Physics

Maths
Physics

“About Myself: I am an undergraduate student at UCL studying Mathematics with Mathematical Physics. Hoping to go into research after my degree, I have a true passion for my subjects and my aim is to pass on that passion to students in ...”

You may also like...

Other A Level Maths questions

How do I do integration by substitution?

How do I find the equation of a tangent to a given point on a curve?

Find the general solution, in degrees, of the equation 2 sin(3x+45°)= 1

How do you differentiate 2 to the power x?

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

mtw:mercury1:status:ok