Question

What does $\dfrac{dy}{dx}$ mean?

Answer 1

Hint: In order to find the solution of this question we should have the knowledge of the concept of differentiation. After this we will be able to explain the concept of $\dfrac{dy}{dx}$. After this we can proceed to learn its formula and mathematical concept.

Complete step by step solution:
It basically denotes the derivative of one variable with respect to another variable where one variable is an independent variable and the other variable is a dependent variable. It is also said to be the slope of the line.
Derivatives are the result of performing a differentiation process upon a function or an expression. Derivative notation is the way we express derivatives mathematically. Derivatives are majorly all about change.
Remember $\dfrac{dy}{dx}$ is the derivative of y with respect to x in simple terms. If $y=f(x)$ is a function of x then the symbol is defined as $\dfrac{dy}{dx}=\displaystyle \lim_{h \to 0}\dfrac{f(x+h)-f(x)}{h}$ and this is again called the derivative of y or f and we can also see that again it is a function of x. On their own, dy and dx does not have any meaning but the symbol $\dfrac{d}{dx}$ can be said as an operator. You can apply this operator to a (differentiable) function. And you get a new function. So, if f is a (differentiable) function that it makes sense to apply $\dfrac{d}{dx}$ to f and write $\dfrac{d}{dx}f$.
Now, we must know that derivative is the rate of change and is the fundamental solution of problems in various fields.

Note: Derivative and antiderivative plays the important role in mathematics so be clear with the terms and concepts of this topic. Initially, we must be aware of the derivative and their properties as how they work for various types of functions.