Q. 3 G4.5( 4 Votes )

Differentiate the following from first principles


Answer :

We need to find derivative of f(x) = x2 ex


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


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


derivative of f(x) = x2 ex is given as –


f’(x) =


f’(x) =


f’(x) =


Using algebra of limits, we have –


f’(x) =



As 2 of the terms will not take indeterminate form if we put value of h = 0, so obtained their limiting value as follows –


f’(x) = 0×ex + 0 + 2x ex + 0 +


Use the formula:


f’(x) = 2x ex + x2 ex


f’(x) = 2x ex + x2 ex


Hence,


Derivative of f(x) = x2 ex = 2x ex + x2 ex


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