1. Differential
In calculus, the differential represents the change in a function y = f(x) with respect to changes in the independent variable. The differential dy is defined by
dy=f'(x)dx
2. Derivative
The derivative of a function of a single variable at a chosen input value, when it exists, is the slope of the tangent line to the graph of the function at that point. For this reason, the derivative is often described as the “instantaneous rate of change”, the ratio of the instantaneous change in the dependent variable to that of the independent variable.–Wikipedia
Derivatives are a fundamental tool of calculus. For example, the derivative of the position of a moving object with respect to time is the object’s velocity: this measures how quickly the position of the object changes when time advances.
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\frac{d y}{d x}=\lim _{\Delta x \rightarrow 0} \frac{\Delta y}{\Delta x}=\lim _{\Delta x \rightarrow 0} \frac{f(x+\Delta x)-f(x)}{\Delta x}=f^{\prime}(x)
dxdy?=limΔx→0?ΔxΔy?=limΔx→0?Δxf(x+Δx)?f(x)?=f′(x)
3. Difference Between Differential and Derivative
In simple words, the rate of change of function is called as a derivative and differential is the actual change of function.
We can also define derivative in terms of differentials as the ratio of differentials of a function by the differential of a variable.
A derivative is the change in a function(dy/dx); a differential is the change in a variable(dx). A function is the relationship between two variables, so the derivative is always a ratio of differentials.
–Quora
4. Calculus
Calculus is the study of how things change. Calculus mainly has two part differential calculus and integral calculus. Calculus is the study of change, rate of change and Accumulation. Rate of change means derivatives and accumulation is integral. Calculus is all about the rate. Learn the rate of change time vs distance, time vs velocity etc. –Medium
For example, the concept of speed of motion is a notion straight from calculus, though it surely existed long before calculus did, and you know lots about it.
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