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# Derivative of Tanx?

TopThe equation which forms Derivatives that are in relation with ordinary and partial derivatives are known as differential equation. In the equation if ordinary derivatives are present then this types of equation is known as differential equation. Let’s talk about the derivative of a function f (s) which is given by:

$\frac{d}{ds}$ f(s)

or

f'(s)

This given function is also known as derivative or we can say differentiation with respect to‘s’. In some cases the differentiation of a function f (s) is known as differentiation coefficient of f (s).

Now we will talk about the derivative of tanx.

The derivative of tan x is shown below:

$\frac{d}{dx}$ Tan x

= sec2 x.

Now we will see the proof of derivative of tanx. If we want to find the derivative of tan x than it is necessary to find the derivative of sin x and cos x because we know that tan x = $\frac{sin x}{cos x}$; so by using quotient rule:

So we can write it as:

$\frac{d}{dx}$ Tan x = $\frac{ cos x \frac{d}{dx} sin x - sin x \frac{d}{dx} cos x}{(cos x)^{2}}$

We know that differentiation of sin (x) is cos (x) and differentiation of cos (x) is – sin (x). So put the value of sin (x) and cos (x) in the above expression.

[(cos (x) cos (x) + sin (x) sin (x))] / cos2 (x);

We can write it as:

= 1 + tan2 (x);

We know that 1 + tan2 (x) = sec2 x;

This is all about derivative of tan x.