Question

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

Answer 1

Hint : As we know that the above question is related to differentiation. It can be defined as the derivative of independent variable value and it can be used to calculate features in an independent variable per modification. Integration and differentiation are the reverse process of each other. These are used to solve the differential equations.

Complete step by step solution:
We know that a differential equation is an equation which has a function and one or more of its derivative or we can say that it is defined as the equation that contains the derivative of one or more dependent variables with respect to one or more independent variables. As for example we have; $y + \dfrac{{dy}}{{dx}} = 5x$ . It is a differential equation with function $y$ and its derivative $\dfrac{{dy}}{{dx}}$ . IN this equation $x$ is an independent variable and $y$ is a dependent variable.
Hence $\dfrac{{dy}}{{dx}}$ is the derivative of the differential equation with function $y$

Note : We should note that $\dfrac{{dy}}{{dx}}$ is defined as the infinitesimal change in $y$ due to an infinitesimal change $dx$ in the value of $x$ . It is called Leibniz's notation. It is commonly used in the differentiation. There are some of the fundamental rules of the differentiation such as sum or difference rule, product rule, chain rule. We need to understand these rules before solving the questions of differentiation and integration.