Calculus Made Easy · Silvanus P. Thompson

Note to Chapter III

6 of 27 · 1 min of reading

It will never do to fall into the schoolboy error of thinking that dx means d times x , for d is not a factor-it means "an element of" or "a bit of" whatever follows. One reads d x thus: "dee-eks."

In case the reader has no one to guide him in such matters it may here be simply said that one reads differential coefficients in the following way. The differential coefficient (d y)/(d x) is read “dee-wy by dee-eks,” or “dee-wy over dee-eks.”

So also (d u)/(d t) is read "dee-you by dee-tee." Second differential coefficients will be met with later on. They are like this: (d^2 y)/(d x^2); which is read “dee-two-wy over dee-eks-squared,” and it means that the operation of differentiating y with respect to x has been (or has to be) performed twice over.

Another way of indicating that a function has been differentiated is by putting an accent to the symbol of the function. Thus if y=F(x) , which means that y is some unspecified function of x (see p. 13 ), we may write F^(′)(x) instead of d(F(x))/dx . Similarly, F^(′ ′)(x) will mean that the original function F(x) has been differentiated twice over with respect to x .

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End of part 6 of 27