Sec X Differentiation

Hii Guys , Here Will you please Provide me X factor Differentiation CSC, Sec and Cot Functions information with Example , Can you please Provide me same ?

[Shaleen]

The Differentiation of Trigonometric Functions is the Mathematical Process of Finding the Derivative of a Trigonometric Function, or its rate of change with respect to a variable.

Common Trigonometric functions Include
sin(x),
cos(x)
tan(x).

For Example, the Derivative of f(x) = sin(x) is represented as f ′(a) = cos(a). f ′(a) is the rate of change of sin(x) at a particular point a.



Differentiation of Trigonometric Functions

It is possible to find the derivative of trigonometric functions.

Here is a list of the derivatives that you need to know:

d (sin x) = cos x
dx

d (cos x) = –sin x
dx

d (sec x) = sec x tan x
dx

d (cosec x) = –cosec x cot x
dx

d (tan x) = sec²x
dx

d (cot x) = –cosec²x
dx

One condition upon these results is that x must be measured in radians.

Applying the Chain Rule

The chain rule is used to differentiate harder trigonometric functions.

Example

Differentiate cos³x with respect to x.
Let y = cos³x
Let u = cos x
therefore y = u³
dy = 3u²
du

du = -sin x
dx

dy = du × dy
dx dx du
= -sin x × 3u²
= -sin x × 3cos²x
= -3cos²x sin x