Differentiate the following from first principle.

xe^x

We need to find derivative of f(x) = xe^x

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

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

∴ derivative of f(x) = xe^x is given as –

f’(x) =

⇒ f’(x) =

⇒ f’(x) =

Using algebra of limits, we have –

⇒ f’(x) =

⇒ f’(x) =

Again Using algebra of limits, we have –

⇒ f’(x) =

Use the formula:

⇒ f’(x) = e^x + xe^x

⇒ f’(x) = e^x(x + 1)

Hence,

Derivative of f(x) = xe^x = e^x(x + 1)