Why you differentiate problems in maths?

Answer 1

Firstly, and most simply, it may lead to another part of a problem or question or context.

Secondly, and importantlyest, (i just invented that word it means most importantly) It can be used to find the gradient of a curve.

As you may know, the gradient of a straight line is constant

y=mx+c the gradient is m

But for a curve, the gradient is always changing.

look at a graph of y=x2 and you will see that an infinite tangents make up the curve each with a different value for m.

In short, when you differentiate a function or equation, you get the gradient function, which allows you to find the gradient at any point on the graph y=f(x)

differentiate y=x2 (which is the same as find dy/dx)

dy/dx=2x

so the gradient on the curve y=x2 always 2 times the x value in question. At x=1 the gradient is 2. At x=2 the gradient is 4.

In mechanics, if you draw a graph of displacement against time for a moving object, the GRADIENT is equal to the function of velocity. Plot velocity against time and the gradient is equal to Acceleration against time.

In any circumstance where a curve is involved differentiation is needed to ind a gradient.

Phew, hope that helps and answers your question