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vazorg [7]
4 years ago
7

(a) Find the differential dy.

Mathematics
1 answer:
Step2247 [10]3 years ago
5 0

a. Practically speaking, you compute the differential in much the same way you compute a derivative via implicit differentiation, but you omit the variable with respect to which you are differentiating.

y=\cos x\implies\boxed{\mathrm dy=-\sin x\,\mathrm dx}

Aside: Compare this to what happens when you differentiate both sides with respect to some other independent parameter, say t:

\dfrac{\mathrm dy}{\mathrm dt}=-\sin x\dfrac{\mathrm dx}{\mathrm dt}

b. This is just a matter of plugging in x=\dfrac\pi3 and \mathrm dx=0.1.

\boxed{\mathrm dy\approx-0.087}

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