Derivative Formula

What is Derivative?

The value that represents the rate of change of function with respect to any variable is called the derivative.

How are the Derivatives Represented?

The derivatives are represented as (d/dx) or if f(x) is a function then, derivative of f(x) is represented as f'(x).

How is the Derivative of a Constant Calculated?

The derivative of a constant is always zero. In mathematical notation, if ‘C’ is a constant, then dC/dx = 0.

Write the General Derivative Formula of xⁿ.

The general formula for derivative of xⁿ = nx^n-1.

How to Calculate the Derivatives of Function?

To calculate the derivatives of a function, we can apply derivatives formula according to given function.

What is the Formula for Derivative of Logarithmic Function?

The derivative of the natural logarithm function, ln(x), is 1/x. In mathematical notation, if y = ln(x), then dy/dx = 1/x.

Which Formula is used to Find Derivative of Exponential Functions?

The derivative of an exponential function, y = a^x (where ‘a’ is a constant), is found using the formula dy/dx = a^x × ln(a).

What are Higher-Order Derivatives?

Higher-order derivatives are derivatives of a function taken more than once. The second derivative is the derivative of the first, the third is the derivative of the second, and so on.

What is Derivative Formula for e^x?

The derivative of the function f(x) = e^x (where ‘e’ is Euler’s number, approximately 2.71828) is simply f'(x) = e^x.

Write Derivative Formula for u/v.

The derivative of the quotient of two functions u(x) and v(x) is given by the quotient rule:

d(u/v)/dx = (v × du/dx – u × dv/dx)/(v²)

What is Derivative Formula for 1/x?

The derivative of the function f(x) = 1/x is given by:

f'(x) = -1/x²

Derivative Formulas in Calculus are one of the important tools of calculus as Derivative formulas are widely used to find derivatives of various functions with ease and also, help us explore various fields of mathematics, engineering, etc.

This article explores all the derivative formulas closely including the general derivative formula, derivative formulas for logarithmic and exponential functions, derivative formulas for trigonometric ratios, derivative formulas for inverse trigonometric ratios, and derivative formulas for hyperbolic functions. Derivative Formula is important for Class 12 students for their Board Exams. We will also solve some examples of derivatives using the different derivative formulas. Let’s closely traverse the topic of Derivative Formula.