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Derivative of Tanx 2?

TopTrigonometric considered as an important branch of mathematics. It shows the relationship among the angles and sides of a triangle. Different type of Trigonometric Functions is defined in this branch of Math.
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 $\frac{d}{dx}$ x2 = 2 sec2 x;

As we know the derivative of tan x is sec2 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 x2.

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) ]/ cos2 (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 ]/ cos2 (x));

On further solving we get:

= $\frac{d}{dx}$ tan x2 = 2 (1 + tan2 (x)) = 2 sec2 x;

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