Among my collection of Maths books, I have found a great AS Maths book which is, at last, really clearly explaining Applications of Differentiation to me.
But I have just reached a part, in a worked example, that I don’t understand.
The question involves a basic formula: r = t2/8 + 1, (the "t2" bit means "t squared") which gives you the radius of an ink spot, the number of seconds after it first appears.
I don’t understand the last bit of the example. They ask you to find “the rate of increase of the radius after 4 seconds”.
They say you need to differentiate, I understand that. But I don’t understand how the derivative that they suggest can be right, as I thought you ignored numbers, eg, 2, 3, etc when finding the derivative.(I understand by the way, why numbers are ignored, it’s because eg, 8 can be considered as 8xo etc) But they have KEPT THE EIGHT in their derivative, and I don’t understand why.
Their derivative is:
Dr/dt = 2t/8 = t/4,
( based on the original function of: r = t2/8 + 1,_("t squared over 8, plus 1)
And so, they say, after 4 seconds the rate of increase is 4/4 = 1 cm per second.
Is their derivative correct? And if it is, I would be grateful if anyone could explain to me why the 8 in the original equation is not just ignored when calculating the derivative?