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.
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.
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.
Some easy rules apply when dealing with functions of functions. A brief discussion follows here.
$$ \frac{d (f(x) + g(x))}{dx} = \frac{df(x)}{dx} + \frac{dg(x)}{dx} $$
$$ \frac{d (f(x) g(x))}{dx} = g(x) \frac{df(x)}{dx} + f(x) \frac{dg(x)}{dx} $$
$$ \frac{d \left(\frac{f(x)}{g(x)} \right)}{dx} = \frac{\frac{df(x)}{dx} g(x) - f(x) \frac{dg(x)}{dx}}{g(x)^2} $$
$$ \frac{d (f(g(x)) }{dx} = \frac{df(y)}{dy} \frac{dy}{dx}$$
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.
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
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