Differential Coefficients of Differential Coefficients

Excerpts

• Differential Coefficients of Differential Coefficients

  has been found, the result, being a function of $x$, may be also differentiated, which gives the differential coefficient of the differential coefficient, or, as it is called, the *second* differential coefficient.

• Differential Coefficients of Differential Coefficients

  Similarly the differential coefficient of the second differential coefficient is called the third differential coefficient, and so on.

• Differential Coefficients of Differential Coefficients

  We have already had occasion to notice these successive differential coefficients in 22, where it appears that $\phi' x$ being the first differential coefficient of $\phi x$, $\phi'' x$ is the coefficient of $h$ in the development $\phi'(x + h)$, and is therefore the differential coefficient of $\phi' x$, or what we have called the second differential coefficient of $\phi x$.

• Differential Coefficients of Differential Coefficients

  In order to avoid so cumbrous a system of notation, the following symbols are usually preferred,

Equations

• Differential Coefficients of Differential Coefficients

  \frac{d^{2} y}{dx^{2}}

  The usual notation for the second differential coefficient of y with respect to x, written in preference to the cumbersome nested d.(dy/dx)/dx form; this is a notation convention, not an equation with an equals sign.

Problems

No exercises in this chapter.