Examples on Derivative of cos2x
Some examples related to derivative of cos2x are,
Example 1: Find the derivative of f(x) = cos2(x2+4)
Solution:
We have, f(x) = cos2(x2+4)
By applying chain rule,
⇒ f'(x) = -2cos(x2+4)×sin(x2+4)×(x2+4)’
⇒ f'(x) = -2cos(x2+4)×sin(x2+4)×(2x)
⇒ f'(x) = -4x.cos(x2+4).sin(x2+4)
Example 2: Find the derivative of f(x) = sec2x
Solution:
Here, f(x) = sec2x can be written as, f(x) = 1/cos2x,
By applying quotient rule, we get,
⇒ f'(x) = (cos2x(1)’ – (1)(cos2x)’)/(cos4x)
⇒ f'(x) = [-2cosx.(-sinx)]/(cos4x)
On simplification, we get
⇒ f'(x) = 2sec2x.tanx
Example 3: Find the derivative of f(x) = xcos2x
Solution:
For f(x) = xcos2x, by applying product rule, we get,
⇒ f'(x) = x(cos2x)’ + (x)’cos2x
⇒ f'(x) = x.(-2cosx.sinx) + cos2x
⇒ f'(x) = cosx.(-2xsinx + cosx)
Derivative of Cos Square x
Derivative of cos2x is (-2cosxsinx) which is equal to (-sin 2x). Cos2x is square of trigonometric function cos x. Derivative refers to the process of finding the change in the cos2x function with respect to the independent variable.
In this article, we will discuss the derivative of cos2x with various methods to find it including the first principle of differentiation, chain rule, and the product rule, solved examples, and some practice problems on it.