Derivative of Tanx

In the previous post we have discussed about Derivative of Cos and In today's session we are going to discuss about Derivative of Tanx, The equation forms derivatives that are in relation with ordinary and partial derivatives are said to be differential equation. Let’s talk about the derivative of a function f (a) which is given by: d/da (f(a)) = limh →0 f (a + h) – f(a) / h; This given function is also known as derivative or we can say differentiation with respect to‘a’. In some cases the differentiation of a function f (a) is known as differentiation coefficient of f (a). Now we will talk about the Derivative of Tanx. The derivative of tan x is given by:

d / dx = tan x = sec2 x.

Let’s discuss 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 is written in the form of sin x / cos x; so by using quotient rule: So we can write it as: Tan x = sin x / cos x; In the derivative form we can write it as:

d/dx Tan x = d/dx (sin x / cos x);

On further solving we get:

(cos (x) d/dx sin (x) – sin (x) d/dx  cos (x)) / cos2 (x);

As 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 we get.

(cos (x) cos (x) + sin (x) sin (x)) / cos2 (x); We can also write it as:

= 1 + tan2 (x);

We know that 1 + tan2 (x) = sec2 x;

Now we will discuss What is a Function in Algebra.  We know that function is used to show the relationship between the given set of elements that is known as domain of a function and the given set of elements is said to be co-domain of a function. To get more information please go through the cbse syllabus for class 9th.