First Principle Of Differentiation Questions And Answers Pdf
The first principle of differentiation is a fundamental concept in calculus that is used to find the slope of a curve at any given point. This principle, also known as the power rule, is a simple yet powerful tool that can be used to find the derivative of any polynomial function. In this article, we will explore the first principle of differentiation in detail and provide answers to some common questions about the topic.
What is the First Principle of Differentiation?
The first principle of differentiation, also known as the power rule, is a formula used to find the derivative of a polynomial function. The formula states that if f(x) = xn, where n is a positive integer, then the derivative of f(x) is given by:
For example, if f(x) = x^2, then the derivative of f(x) is given by:
Therefore, the slope of the curve y = x^2 at the point (1,1) is 2.
Why is the First Principle of Differentiation Important?
The first principle of differentiation is important because it is used to find the slope of a curve at any given point. This information is crucial in many fields, such as physics, engineering, and economics. For example, in physics, the first principle of differentiation is used to find the velocity and acceleration of an object at any given time. In economics, the first principle of differentiation is used to find the marginal cost and marginal revenue of a product.
How is the First Principle of Differentiation Used?
The first principle of differentiation can be used to find the derivative of any polynomial function. To use the formula, simply take the power of x, multiply it by the coefficient, and then subtract one from the power of x. For example, to find the derivative of f(x) = 3x^2, start by taking the power of x (2), multiplying it by the coefficient (3), and then subtracting one from the power of x (1). Therefore, the derivative of f(x) = 3x^2 is 6x.
What are Some Common Mistakes When Using the First Principle of Differentiation?
One common mistake when using the first principle of differentiation is forgetting to subtract one from the power of x. Another common mistake is forgetting to multiply the coefficient by the power of x. It is important to remember these steps in order to find the correct derivative.
Conclusion
The first principle of differentiation is a fundamental concept in calculus that is used to find the slope of a curve at any given point. This principle is important in many fields and is used to find velocity, acceleration, marginal cost, and marginal revenue. It is important to use the formula correctly and avoid common mistakes such as forgetting to subtract one from the power of x or forgetting to multiply the coefficient by the power of x.