Practice Problems on Derivatives
Problem 1: Find the derivative of the function [Tex]f(x) = 3x^2 + 2x – 5 [/Tex]
Problem 2: Calculate the derivative of the function [Tex]g(x) = \sin(x) + \cos(x) [/Tex]
Problem 3: Determine the derivative of the function [Tex]h(x) = e^{2x} [/Tex]
Problem 4: Find the derivative of the function [Tex]k(x) = \ln(x^2 + 1) [/Tex]
Problem 5: Compute the derivative of the function [Tex]m(x) = \frac{3x + 2}{x – 1} [/Tex]
Derivatives | First and Second Order Derivatives, Formulas and Examples
Derivatives: In mathematics, a Derivative represents the rate at which a function changes as its input changes. It measures how a function’s output value moves as its input value nudges a little bit. This concept is a fundamental piece of calculus. It is used extensively across science, engineering, economics, and more to analyze changes.
Table of Content
- What are Derivatives?
- Derivatives Meaning
- Derivative by First Principle
- Types of Derivatives
- First Order Derivative
- Second Order Derivative
- nth Order Derivative
- Derivatives Formula
- Rules of Derivatives
- Derivative of Composite Function
- Chain Rule of Derivatives
- Derivative of Implicit Function
- Parametric Derivatives
- Higher Order Derivatives
- Partial Derivative
- Logarithmic Differentiation
- Applications of Derivatives
- Derivatives Examples
- Sample Problems on Derivatives
- Practice Problems on Derivatives
A derivative is a calculus tool that measures the sensitivity of a function’s output to its input. It is also known as the instantaneous rate of change of a function at a given position.
The derivative of a function with just one variable is the slope of the line that is tangent to the function’s graph for a given input value. In terms of geometry, the derivative of a function can be defined as the slope of its graph.
In this article we have covered Meaning of Derivatives along with types of derivatives, examples, formulas, applications and many more.
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