Here we will see the derivative of tanx 2.

This derivative function is similar to the derivative function of tan x the only difference is Square value. In the last result here we have to put ‘2’.

First we have to write the function Tan x 2 in the derivative form:

So we can write it as:

= tan $\frac{d}{dx}$ x

^{2}= 2 sec

^{2}x;

As we know the derivative of tan x is sec

^{2}x and we can also write tan x in the form of sine and cosine.

It can be written as:

= tan x = sin x / cos x;

Then put these values in place of tan x;

= 2 ($\frac{d}{dx}$ tan x) = 2 ($\frac{sin x}{cos x}$);

Then we have to apply the Product rule to find the derivative of tan x

^{2}.

The division rule is given by:

$\frac{d}{dx}$ $\frac{u}{v}$ = $\frac{ u \frac{dv}{dx} - v \frac{du}{dx} }{u^{2}}$ ;

So we can write it as:

= 2 [(cos x $\frac{d}{dx}$ sin (x) – sin (x) $\frac{d}{dx}$ cos (x) ]/ cos

^{2}(x));

If we differentiate sin x then we get cos x and if we differentiate cos x then we get (– sin x), so put these derivative in the above function we get:

= 2 [(cos x cos x + sin (x) sin x ]/ cos

^{2}(x));

On further solving we get:

= $\frac{d}{dx}$ tan x

^{2}= 2 (1 + tan

^{2}(x)) = 2 sec

^{2}x;

This is how we can solve the derivative of tanx 2. In this way we can find any of the Derivatives.