Examples of Differentiation Formulas
Let’s solve some example problems on the rules of derivative.
Example 1: Find the differentiation of y = 4x3 + 7x2 + 11x + 12
Solution:
Given
- y = 4x3 + 7x2 + 11x + 12
Differentiating with respect to x,
dy/dx = 4(3x2) + 7(2x) + 11(1) + 0
⇒ dy/dx = 12x2 + 14x + 11
This is the required differentiation
Example 2: Find the differentiation of y = cos(log x)
Solution:
Given
- y = cos(log x)
Differentiating with respect to x,
dy/dx = d/dx{cos (log x)}
⇒ dy/dx = sin (log x).{d/dx(log x)}
⇒ dy/dx = sin (log x).(1/x)
This is the required differentiation
Example 3: Find the differentiation of y = tan (3x2 + 4x)
Solution:
Given
- y = tan (3x2 + 4x)
Differentiating with respect to x,
dy/dx = 1/{1 + (3x2 + 4x)2}2 d/dx(3x2 + 4x)
⇒ dy/dx = 1/{1 + (3x2 + 4x)2}2 (6x + 4)
⇒ dy/dx = (6x + 4)/{1 + (3x2 + 4x)2}2
This is the required differentiation
Differentiation Formulas
Differentiation Formulas: Differentiation allows us to analyze how a function changes over its domain. We define the process of finding the derivatives as differentiation. The derivative of any function f(x) is represented as d/dx.f(x)
In this article, we will learn about various differentiation formulas for Trigonometric Functions, Inverse Trigonometric Functions, Logarithmic Functions, etc., and their examples in detail.
Table of Content
- What is Differentiation?
- Differentiation Formula
- Basic Differentiation Formulas
- Differentiation of Trigonometric Functions
- Differentiation of Inverse Trigonometric Functions
- Differentiation of Hyperbolic Functions
- Differentiation Rules
- Differentiation of Special Functions
- Implicit Differentiation
- Higher Order Differentiation
- Examples of Differentiation Formulas
- Practice Problems on Differentiation Formulas