Calculus
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How Derivatives Impact Profit Maximisation

In economics, understanding the relationship between costs, revenues, and profits is crucial for making well-informed decisions. Marginal analysis is one effective way to analyse these relationships. In this method, derivatives play a key role in examining marginal cost, marginal revenue, and profit maximisation. What is Marginal Cost and Revenue? Before you dive into the role…
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A bit more on Implicit Differentiation

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Implicit Differentiation

Differentiating Implicitly Defined Functions In calculus, you often deal with functions where one variable is explicitly written in terms of another. An example is y as a function of x. However, not all relationships between variables are this straightforward. Some equations involve variables that are so intertwined you can’t separate them neatly. These are called…
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Basic differentiation rules

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Solving Problems Involving Multiple Variables

Related Rates When you think about how quantities change over time, you can learn about the relationships between those changes. These relationships can reveal profound insights into the world around you. Related rates are a powerful tool in calculus that help you understand how different variables interact as they evolve. From physics to engineering, the…
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Finding critical points of a polynomial

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Optimization with Derivatives

Finding Maximums and Minimums The goal of optimisation is to identify the optimal solution. This entails maximising a positive outcome, such as profit. It also implies minimising a negative aspect, such as expenses. Derivatives are among the most effective optimization methods in mathematics and real-world problem resolution. You can find significant locations in a function…
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Speed and Velocity – know the difference

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Applications of Derivatives in Physics

Kinematics and Motion Physics and mathematics work together to help us comprehend how things move. The derivative is one of the most potent mathematical instruments in physics. Physicists can better analyse motion by using derivatives. They are able to compute speed variations. Physicists also forecast the behavior of objects in various scenarios. 1. Understanding Motion…
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Chain rule in less than 40 sec
