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RULES FOR DIFFERENTIATING
55
sin
55
Third Step.
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,-
