MYTUTOR SUBJECT ANSWERS

203 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,...

5 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

£20 /hr

Liam R.

Degree: Economics (Bachelors) - Durham University

Subjects offered:Maths

Maths

“I study Economics at Durham. I have a passion for maths and hope to share this with you! To find out more, click on my profile & book a free 15-minute meeting!”

£36 /hr

Joe B.

Degree: Mathematics G100 (Bachelors) - Bath University

Subjects offered:Maths, Further Mathematics + 4 more

Maths
Further Mathematics
Economics
.STEP.
.MAT.
-Personal Statements-

“About Me Hi, I'm Joe, a first year mathematics student from Luton studying at Bath University. I am an accomplished mathematician and economist, having achieved A* grades in A Level Maths, Further Maths and Economics in June 2016. As ...”

£22 /hr

Dan B.

Degree: MPhys Physics (Masters) - Exeter University

Subjects offered:Maths, Physics

Maths
Physics

“Hi I'm Dan and I'm in the first year of a four-year MPhys Physics degree at the University of Exeter. I am very patient and will tailor the sessions' content and pace to suit your individual needs...”

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

M1: A stationary rock is dropped from a height of 30m above the ground. Calculate the time taken to reach the ground and its velocity as it hits the floor.

What is a parametric equation?

Integrate the following function by parts and reduce it to it's simplest form. f(x) = ln(x).

How can we remember the difference between differentiation and integration?

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