Some Other Derivative Formulas

There are some other functions like implicit functions, parametric functions and higher order derivatives whose derivative formulas are listed below:

Implicit Derivative Formula

The method of finding the derivative of an implicit function is called implicit differentiation. Let’s take an example to understand the method of finding derivatives implicitly.

Example: Find derivative of xy = 2

Solution:

(d/dx) [xy] = (d/dx) 2

⇒ x(dy/dx) + y(dx/dx) = 0

⇒ x(dy/dx) + y(1) = 0

⇒ x(dy/dx) + y = 0

⇒ x(dy/dx) = -y

⇒ (dy/dx) = -y/x

From given equation y = 2/x

(dy/dx) = -(2/x)/x

⇒ (dy/dx) = -(2/x²)

Learn more about Implicit Differentiation.

Parametric Derivative Formula

If the function y(x) is expressed in the terms of third variable t and x and y can be represented in the x = f(t) and y = g(t) then, this type of function is called as parametric function.

If y is function of x and x = f(t) and y = g(t) are two differentiable functions of parameter t then, derivative of parametric function is given by:

(dy/dx) = (dy/dt)/(dx/dt), such that (dx/dt) ≠ 0

Read more about Parametric Differentiation.

Higher Order Derivative Formula

Finding the derivative of a function for more than one time gives the higher order derivative of a function.

n^th Derivative = dⁿy/(dx)ⁿ

Read more about Higher Order Derivative.

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.