Question

What is $\dfrac{{dy}}{{dx}}$ ?

Answer 1

$\dfrac{{dy}}{{dx}}$ is an important part of calculus, which is pronounced as “dee y by dee x” known as differentiation. It is divided into two parts, one is the numerator $dy$ which is the small part of $y$ and similarly, for the denominator part $dx$, which is the small part of $x$. Collectively, it is represented as differentiating $y$ with respect to $x$.

Complete step by step answer:
We are given with a value $\dfrac{{dy}}{{dx}}$, we know that it is pronounced as differentiation or derivative of $y$ in terms of $x$ or derivative of $y$ with respect to $x$.Where $y$ can be any kind of a function like ${x^3}$, $5{x^8} + 5x$, ${e^x}$ or etc. There can be any functions and we need to solve the functions with the formulas given in the differentiation rule.

We can also say it as the rate of change of $y$ with respect to $x$. $y$ can also be written in terms of function as $f\left( x \right)$. When differentiated it is represented with a single inverted comma as- $f'\left( x \right)$. $dy$ is nothing but a small change in $y$, similarly, $dx$ is a small change in $x$. There are different rules that are used in differentiation such as: the product rule, the quotient rule, the chain rules, etc. It depends on the type of function that which rule should be used.

Note: The equation $\dfrac{{dy}}{{dx}}$ is Leibniz's notation, which is commonly used to represent differentiation. It’s very important to remember and use the correct formula while calculating differentiation, a small change in formula can lead to big errors. The differentiation of a constant term is always zero.