What is exactly differentiation?

MYTUTOR SUBJECT ANSWERS

Answers / Maths / A Level / What is exactly differentiation?

588 views

What is exactly differentiation?

This is obviously a very important but somewhat difficult to explain question of maths. Let's try to define these terms for normal functions between R (real numbers) and R.

Now, if we consider the derivative of f at a certain point (let's say x), you can think of it as looking at the gradient of f at that point. So, if you're function f is constant, then we have a flat line, and so we have that it's gradient everywhere is 0, and therefore it's derivative is zero. (i.e. f'(x) = 0 for all x). If, however we have a linear function such as f(x) = 2x + 1, if we look at the graph we see that it's gradient is 2 (using the simple gradient formula), hence f'(x) = 2.

Of course we don't have to use the gradient formula every time, sometimes we won't even be able to (when the function isn't linear, that is), and there is a very helpful rule for functions of the type f(x) = x^n.

That is, f'(x) = nx^(n-1).

But it is still good to understand what the derivative really is, once you understand it's relationship with the gradient, you will already be ahead of most other A-level mathematicians. Indeed, have you ever wondered why f has a minimum at x if f'(x) = 0? Draw a picture of f and what it looks like when the gradient is 0 at a certain point, and it will all become natural.

Joseph P. GCSE Maths tutor, A Level Maths tutor, GCSE French tutor, U...

1 year ago

Answered by Joseph, an A Level Maths tutor with MyTutor

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

322 SUBJECT SPECIALISTS

Scott R. GCSE Maths tutor, 13 Plus Maths tutor, A Level Maths tutor,...

View profile

£26 /hr

Scott R.

Degree: PGCE Secondary Mathematics (Other) - Leeds University

Subjects offered:Maths, Further Mathematics

“I am currently completing 2 PGCEs in Leeds. I have always had a passion for maths and my objective is to help as many as possible reach their full potential.”

5.0

18 reviews | 77 completed tutorials

Save profile

Giorgos A. A Level Maths tutor, GCSE Maths tutor, A Level Physics tut...

View profile

£20 /hr

Giorgos A.

Degree: Mechanical Engineering with Renewable Energy (Masters) - Edinburgh University

Subjects offered:Maths, Physics

“Feel rewarded helping younger students. Nobody is born knowing everything, life is a learning process and my aim is to help you achieve your goals.”

Trusted by schools

| 5 completed tutorials

Save profile

View profile

£20 /hr

Javed R.

Degree: Biomedical Engineering (Bachelors) - Liverpool University

Subjects offered:Maths, Chemistry

“Postgraduate Biomedical Engineering student at the University of Strathclyde. Past classroom experience.”

5.0

2 reviews | 40 completed tutorials

Save profile

See more A Level Maths tutors

About the author

View profile

Joseph P.

Currently unavailable: for regular students

Degree: Mathematics (Bachelors) - Warwick University

Subjects offered:Maths, French+ 1 more

“About MeI am a 20 year old mathematics student at the University of Warwick, about to enter my final year. Though I have always enjoyed a range of subjects (from Latin to Music) I have a particular fondness for maths, and have much ...”

5.0

3 reviews | 8 completed tutorials

Save profile

Version:	3.47.1
Build:	245b6290c38f
Time:	2017-07-12T13:15:28Z

MYTUTOR SUBJECT ANSWERS

What is exactly differentiation?

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

322 SUBJECT SPECIALISTS

About the author

You may also like...

Posts by Joseph

Other A Level Maths questions

One-to-one help is at your fingertips