Q. 1 K5.0( 1 Vote )

Differentiate each of the following from first principles:

(x + 2)3

Answer :

We need to find the derivative of f(x) = (x + 2)3


Derivative of a function f(x) from first principle is given by –


f’(x) = {where h is a very small positive number}


derivative of f(x) = (x + 2)3 is given as –


f’(x) =


f’(x) =


Using a3 – b3 = (a – b)(a2 + ab + b2)


f’(x) =


f’(x) =


As h is cancelled, so there is no more indeterminate form possible if we put value of h = 0.


So, evaluate the limit by putting h = 0


f’(x) =


f’(x) = (x + 0 + 2)2 + (x + 2)(x + 2) + (x + 2)2


f’(x) = 3 (x + 2)2


f’(x) = 3 (x + 2)2


Hence,


Derivative of f(x) = (x + 2)3 is 3(x + 2)2


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses