Other Types of
Derivatives
Trigonometric
Inverse Trigonometric
Hyperbolic
Inverse Hyperbolic
Objective
At the end of the lesson, you should be able to:
• Know how to perform differentiating trigonometric, hyperbolic and their
inverse
• How to apply these types of derivatives in your chosen field
• Understand why they are important in your chosen field
First things first
You must be familiar with these identities
First things first
You must be familiar with these formula
Trigonometric Functions
Derivatives of Trigonometric Functions
Trigonometric Functions
Derivatives of Trigonometric Functions
Example:
Find the derivative of the following functions:
1. y = cos 4x
2. y = sq. rt. cos x
3. y =
cos 𝑥
csc 𝑥
4. y = sin (tan x)
5. 𝑦 = sin 3 𝑥 + sin 3 𝑥
Inverse Trigonometric Functions
Derivatives of Inverse Trigonometric Functions
Inverse Trigonometric Functions
Derivatives of Inverse Trigonometric Functions
Example:
Find the derivative of the following functions:
1. y =
sin−1 (𝑥)
1+𝑥
2. y= sin-1 (2x+1)
Hyperbolic Functions
Derivatives of Hyperbolic Functions
Hyperbolic Functions
Derivatives of Hyperbolic Functions
Example:
Find the derivative of the following functions:
1. y =
𝑥+1
tanh(𝑥)
2. y = tanh((2x+3)2)
Inverse Hyperbolic Functions
Derivatives of Inverse Hyperbolic Functions
Hyperbolic Functions
Derivatives of Hyperbolic Functions
Example:
Find the derivative of the following functions:
1. y = cosh−1 (𝑥 2 + 1)
2. y = sinh−1 (coth 𝑥 2 )
Problem-solving Questions
Example: Answer the following questions, show your solutions.
Example 1
The apparent power Pa of an electric circuit whose
power is P and whose impedance phase angle is θ, is
given by
Pa =P sec θ
Given that P is constant at 12 W, find the time rate of
change of Pa if θ is changing at the rate of 0.050
rad/min, when θ = 40°.
Problem-solving Questions
Example: Answer the following questions, show your solutions.
Example 2
A ladder 15 ft long leans against a vertical wall.
If the top slides down at 2 ft/sec, how fast is
the angle of elevation of the ladder decreasing,
when the lower end is 12 ft from the wall?
Problem-solving Questions
Example: Answer the following questions, show your solutions.
Example 3
Differentiate 𝑦 = 𝑥 3 tanh2 𝑥
Problem-solving Questions
Example: Answer the following questions, show your solutions.
Example 4
Evaluate the derivative of the function tanh−1 (cos 3𝑥) .