Differentiate the following from first principle.
e3x
We need to find derivative of f(x) = e3x
Derivative of a function f(x) is given by –
f’(x) = {where h is a very small positive number}
∴ derivative of f(x) = e3x is given as –
f’(x) =
⇒ f’(x) =
⇒ f’(x) =
Taking e – x common, we have –
⇒ f’(x) =
Using algebra of limits –
⇒ f’(x) =
As one of the limits can’t be evaluated by directly putting the value of h as it will take 0/0 form.
So we need to take steps to find its value.
⇒ f’(x) =
Use the formula:
⇒ f’(x) = e3x × (3)
⇒ f’(x) = 3e3x
Hence,
Derivative of f(x) = e3x = 3e3x