**Example :** Using the first principal find the differential coefficient of y = f (x), where f (x) is

(i) e^{x}

(ii) tan x

(iii) sinx/x

(iv) tan^{−1} x

**Solution :**

(i) y = f (x) = e^{x}

we have, f ‘ (x) =

(ii) y = f (x) = tan x

We have , f ‘ (x) =

=

= sec^{2}x

(iii) y = f (x) = sinx/x

We have , f ‘ (x) =

=

(iv) y = f (x) = tan^{−1} x

we have , f ‘ (x) =

=