Differentiation from first principles

Differentiaiton from principles requires the use of the following formula which is provided in the formula booklet:

f'(x) = limh->0 ((f(x+h) - f(x))/(h))

Consider a function:

f(x) = 6x2

Clearly we know that the function differentiates to:

f'(x) = 12x 

by using the process of multiplying the coefficient by the power and then reducing the power by 1.

Using first principles however we must consider the formula mentioned previously.

f'(x) = limh->0 ((f(x+h) - f(x))/(h))

By computing the function for x+h and x we get:

f'(x) = limh->0 (6(x+h)2 - 6x2)/(h))

f'(x) = limh->0 (6(x2+2xh+h2) - 6x2)/(h))

f'(x) = limh->0 (6x2+12xh+6h2) - 6x2)/(h))

f'(x) = limh->0 (12xh+6h2)/(h))

We now cancel the h from above and below to get:

f'(x) = limh->0 12x+6h

Now consider the limit as h-> 0, clearly 12x remains unaffected but 6h will become 0 and is hence removed. Hence we are left with:

f'(x) = 12x

Which we know to be true from the trivial methods of differentiation considered earlier. 

Hanumanth Srikar K. IB Further Mathematics  tutor, IB Maths tutor, GC...

8 months ago

Answered by Hanumanth Srikar, an IB Maths tutor with MyTutor

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


Marco-Iulian G. GCSE Maths tutor, Uni Admissions Test .MAT. tutor, A ...
View profile
£20 /hr

Marco-Iulian G.

Degree: Mathematics&Computer Science (Masters) - Bristol University

Subjects offered: Maths, Further Mathematics + 2 more

Further Mathematics

“I'm in my first year at University of Bristol, studying Mathematics and Computer Science MEng. From an early age I started to participate in lots of contests and maths olympiads, and the experience I achieved along the way enriched bo...”

Gabriela S. GCSE Maths tutor, IB Maths tutor, IB Economics tutor, IB ...
View profile
£20 /hr

Gabriela S.

Degree: Economics (Bachelors) - Durham University

Subjects offered: Maths, History+ 2 more


“About Me I’m an economics student at Durham University. I love learning new things, teaching them to other people and trying to make everything as interesting and understandable as possible! I really enjoy everything related to econom...”

PremiumTom J. A Level Economics tutor, IB Economics tutor, GCSE Economics tu...
View profile
£24 /hr

Tom J.

Degree: MSc Ecological Economics (Masters) - Edinburgh University

Subjects offered: Maths, Philosophy+ 2 more


“I have fostered a passion for teaching ever since taking the opportunity to travel to China and teach at an English language school for Chinese pupils.  This experience not only massively broadened my horizons culturally, but also gav...”

About the author

Hanumanth Srikar K. IB Further Mathematics  tutor, IB Maths tutor, GC...
View profile

Hanumanth Srikar K.

Currently unavailable: for new students

Degree: Maths and Economics (Bachelors) - LSE University

Subjects offered: Maths, German+ 3 more

Further Mathematics

“Hanumanth Srikar Karri - London School of Economics”

You may also like...

Posts by Hanumanth Srikar

Differentiation from first principles

Factorising a Quadratic

Other IB Maths questions

How do you calculate the probability P(X < x) for a normally distributed random variable X?

Differentiation from first principles

Solve the equation 8^(x-1) = 6^(3x) . Express your answer in terms of ln 2 and ln3 .

Show that the following system of equations has an infinite number of solutions. x+y+2z = -2; 3x-y+14z=6; x+2y=-5

View IB 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