Introduction – Derivatives

Derivatives is also one of the important lessons in Calculus.  It is fundamental to the solution of problems in Calculus and differential equations. A derivative is the rate of change of a function with respect to a variable.

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Derivatives:

Derivatives play an important role in keeping the transaction costs low in the market. The cost of trading derivatives has to be kept low, thereby bringing down the overall transaction costs of the market. Derivatives also offer other benefits like bringing liquidity to the market and encouraging short selling.

Real-life application of Derivatives

Derivatives play a significant role in calculating profit and loss in business.

You think of factors such as the rate of change of customers, the expenses, the days of sales, and etc. Derivatives help you easily calculate all of these business calculations and saves you a headache in the process.

Sub-Topics List:

Derivative of a Function to the Slope of the Tangent Line

Rules for Differentiation

Differentiation of Algebraic, Exponential, and Trigonometric Functions

Higher-Order Derivatives of Functions

Chain Rule of Differentiation

Implicit Differentiation

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references

Derivative of a Function to the Slope of the Tangent Line

A tangent line is a straight line that touches a function at only one point. It also represents the instantaneous rate of change of the function at that one point. The slope of the tangent line at a point on the function is equal to the derivative of the function at the same point.

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Rules for Differentiation

The basic derivative rules.

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Differentiation of Algebraic, Exponential, and Trigonometric Functions

Exponential function

Logarithmic Function

Trigonometric Function

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Higher-Order Derivatives of Functions

A higher-order derivative means the derivatives other than the first derivative and are used to model real-life phenomena like most transportation devices.

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Chain Rule of Differentiation

The Chain Rule tells us how to find the derivative of a composite function. A function is composite if it is a function within a function, or a function of a function. The chain rule says:

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Implicit Differentiation

In Implicit Differentiation, we differentiate each side of an equation with two variables by treating one of the variables as a function of the other. This calls for using the chain rule.

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