Question

Differentiate the following from first principles

e^{√(ax + b)}

Answer 1

We need to find derivative of f(x) = e^{√(ax + b)}

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

{where h is a very small positive number}

∴ derivative of f(x) = e^{√(ax + b)} is given as –

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.

∴ multiplying numerator and denominator by  in order to apply the formula –

Again we get an indeterminate form, so multiplying and dividing √(ax + ah + b) + √(ax + b) to get rid of indeterminate form.