# Rules for finding derivatives

##### Calculus

Derivatives of some functions are well-known. Using such well-known derivatives with some simple rules explained in this article, it is easy to arrive at the derivative of more complicated functions.

## Prerequisites

To understand the rules for finding derivaties, we recommend familiarity with the concepts in

Follow the above links to first get acquainted with the corresponding concepts.

### Rules for computing derivatives

Some easy rules apply when dealing with functions of functions. A brief discussion follows here.

• The Sum rule helps in calculating the derivative of the sum of two functions, if they are differentiable.

$$\frac{d (f(x) + g(x))}{dx} = \frac{df(x)}{dx} + \frac{dg(x)}{dx}$$

• The Product rule helps in calculating the derivative of the product of two functions, if they are differentiable.

$$\frac{d (f(x) g(x))}{dx} = g(x) \frac{df(x)}{dx} + f(x) \frac{dg(x)}{dx}$$

• The Quotient rule is used to calculate the derivative of the ratio of two differentiable functions.

$$\frac{d \left(\frac{f(x)}{g(x)} \right)}{dx} = \frac{\frac{df(x)}{dx} g(x) - f(x) \frac{dg(x)}{dx}}{g(x)^2}$$

• The Chain rule is used to compute the derivative of a function of a function. If we use the symbol $y = g(x)$, and if $f'(y)$ and $g'(x)$ exists, then we can write

$$\frac{d (f(g(x)) }{dx} = \frac{df(y)}{dy} \frac{dy}{dx}$$

More generally, one can write

These rules are the building blocks for computing derivatives of complicated functions from the derivatives of well-known simpler functions.

## Where to next?

Now that you are an expert in derivatives, explore the counterpart to derivatives — integrals.

Already a calculus expert? Check out comprehensive courses on multivariate calculus, machine learning or deep learning