Differentiation Rules
Various rules of finding the derivative of functions have been given below:
| Rules | Function Form (y =) | Differentiation Formula (dy/dx =) |
|---|---|---|
| Sum Rule | u(x) ± v(x) | du/dx ± dv/dx |
| Product Rule | u(x) × v(x) | u dv/dx + v du/dx |
| Quotient Rule | u(x) ÷ v(x) | (v du/dx – u dv/dx) / v² |
| Chain Rule | f(g(x)) | f'[g(x)] g'(x) |
| Constant Rule | k f(x), k ≠ 0 | k d/dx f(x) |
Differentiation of Special Functions
If we have two parametric functions x = f(t), y = g(t), where t is the parameter, then the differentiation of parametric functions is as follows,
As dy/dt = g'(t) and dx/dt = f'(t) then dy/dx is given by:
dy/dx = (dy/dt)/(dx/dt) = g'(t)/f'(t)
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
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