Question

What is \[\dfrac{{dy}}{{dx}}\]?

Answer 1

Hint: In this question, we need to define the concept of \[\dfrac{{dy}}{{dx}}\] . Here, we need to explain the concept of derivative that consists of independent and dependent variables. In this case, \[y\] is dependent variable and \[x\] is independent variable.

Complete step-by-step solution: We have been given the term \[\dfrac{{dy}}{{dx}}\].
Let us see the significance of it.
Basically, \[\dfrac{{dy}}{{dx}}\] indicates the derivative of \[y\] with respect to \[x\]. That is the rate of change of variable \[y\] with respect to \[x\] .
The derivative of a function is a function that illustrates the rate of change of another function.
So, the finding derivative of a function is differentiation.
Therefore, it is possible to find the derivative of a function using the concept of differentiation.
Also, the slope of a function is denoted by the derivative of a function.

Therefore, \[\dfrac{{dy}}{{dx}}\] indicates the change in variable \[y\] with respect to \[x\].

Additional Information : The derivatives can be used to determine the equation of tangent and normal line to a function's curve. A function's derivative can be used to provide the linear approximation of a function at a specific value. Also, for determining whether the given function is increasing or decreasing, differentiation is used. Also, this concept can be useful for determining the maximum or minimum values of a given function.

Note: The term \[\dfrac{{dy}}{{dx}}\] represents that the derivative of \[y\] with respect to the variable \[x\]. It is also denoted by \[y'\]. Here, the derivative function computes a function's derivative at every point in the domain of the primary function for which the derivative is specified.