Question

Differentiate the following from first principles

a^√x

Answer 1

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

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

{where h is a very small positive number}

∴ derivative of f(x) = a^√x 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 \(\sqrt{x+h}-\sqrt{x}\) in order to apply the formula – 

Again we get an indeterminate form, so multiplying and dividing

√(x + h) + √(x) to get rid of indeterminate form.