Differentiate the following from first principle.
xex
We need to find derivative of f(x) = xex
Derivative of a function f(x) is given by –
f’(x) = {where h is a very small positive number}
∴ derivative of f(x) = xex 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) = ex + xex
⇒ f’(x) = ex(x + 1)
Hence,
Derivative of f(x) = xex = ex(x + 1)