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


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

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