Some Other Trig Function Derivatives

The differentiation of the trigonometric functions can be easily done using chain rule. The complex trigonometric functions and composite trigonometric functions can be solved by applying chain rule of differentiation. In the following headings we will further study about the chain rule and composite trig functions differentiation in detail.

• Differentiation using Chain Rule
• Differentiation of Composite Trig Function

Let’s discuss these topics in detail.

Chain Rule and Trigonometric Function

The chain rule states that if p(q(x)) is a function then, the derivative of this function is given by the product of the derivative of p(q(x)) and derivative of q(x). The chain rule is used to differentiate composite functions. The chain rule is mostly used to differentiate the composite trig functions easily.

Example: Find the derivative of f(x) = tan 4x

Solution:

f(x) = tan 4x

⇒ f'(x) = (d/dx) [tan 4x]

By applying chain rule

f'(x) = (d/dx) [tan 4x](d/dx)[4x]

⇒ f'(x) = (sec² 4x)(4)

Differentiation of Composite Trig Function

To evaluate the differentiation of the composite trig functions we apply chain rule of differentiation. The composite trig functions are the functions in which the angle of the trigonometric function is itself a function. The differentiation of composite trigonometric functions can be easily evaluated by applying the chain rule and the differentiation formulas for trig functions.

Example: Find the derivative of f(x) = cos(x² +4)

Solution:

f(x) = cos(x² +4)

⇒ f'(x) = (d/dx) cos(x² +4)

By applying chain rule

f'(x) = (d/dx) [cos(x² +4)](d/dx)[x² +4]

⇒ f'(x) = -(2x)sin(x² +4)

Differentiation of Trigonometric Functions is the derivative of Trigonometric Functions such as sin, cos, tan, cot, sec, and cosec. Differentiation is an important part of the calculus. It is defined as the rate of change of one quantity with respect to some other quantity. The differentiation of the trigonometric functions is used in real life in various fields like computers, electronics, and mathematics.

In this article, we will learn about the differentiation of trigonometric functions along with the formulas, their related proofs, and their applications. Also, we will solve some examples and get answers to some FAQs on the differentiation of trigonometric functions. Let’s start our learning on the topic of Differentiation of Trigonometric functions.