Page:Elements of the Differential and Integral Calculus - Granville - Revised.djvu/79

Rh sin

55

Rh

FOURTH STEP.

Since

=

dv

= cos v.



Since v is a function of # and it is required to differentiate sinv with respect to x, we must use formula (-4.), 42, for differentiating a function of a function, namely,

dy dy dv

' rrs < -

cfo dv dx

Substituting value -~ from Fourth Step, we get dv

XI

d

dx

dy dv

-- = cos v - ax ax

dv

dx

The statement of the corresponding rules will now be left to the student.

49. Differentiation of cos v.

Let y = cos v.

By 29, p. 2, this may be written

Differentiating by formula XI,

dy _ (TT dlir ~dx = * '7<fe""7

. dv

= sin v dx

[since cos (^ - v^ = sin w, by 29, p. 2.1

. dv = -sin,-