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ELI5:Why exactly do we need differential calculus?

I have just started learning calculus, and I get the gist of differentiation and integration and stuff, but why exactly do we need to use it ? I mean, for example, velocity/time is already acceleration, so why can't we just use that in place of dv/dt?
gpt
It is no exaggeration to say that anything university level that requires mathematics will need calculus.   In fact it is probably the basics of what you need.  Things only get more complicated from there.

Differentiation is basically calculating a rate of change.  Turn that around and you get integration, which basically allows you to find out different things given a function, i.e. a graph.  It is easy to calculate the area under a graph if it is a straight line.  Once it becomes more complicated, like a curve, then it becomes more difficult. So you use integration.

Many topics in advanced education begin to use mathematical models to define things.  Even things you wouldn't expect. And often these mathematical models will involve the use of calculus.  For example, in psychology you are often required to take statistics, which uses calculus.  Even in a management class you can be given a formula which may model a market or effect of change in prices on demand.  **These will use calculus to find an optimal solution to something.**

How would that work? well we know differentiation is finding the function that defines the rate of change.  How would you find the optimal solution to a function; say the profitability of a product is defined by a curved function; it goes up, then starts slowing down (i.e. curving) before going down, due to the idea of diminishing returns.  

What would be the optimal solution? how do you find the "peak"? well that is simple.  You find the precise point where the rate of change is 0; it is the precise point from when it increases to decreases.  The peak of the curve. 

What happens if you differentiate that profit function? you are finding the marginal profit; how much more profit you get per unit of production.

What happens if you integrate that function? you get the total amount of profit.  You can even use it to define the amount of profit you get at different points of the curve.