An example of implicit differentation in Stewart, 6th ed, p 883, is given as follows:(adsbygoogle = window.adsbygoogle || []).push({});

x^3 + y^3 + z^3 + 6xyz = 1

Differentiating to find dz/dx,

3x^2 + 3z^2(dz/dx) + 6yz + 6xy(dz/dx) = 0

where the product rule was used to differentiate 6xyz with respect to x.

Why isn't the product rule also used when differentiating explicitly?

e.g.

if z = xy, dz/dx = y.

rather than dz/dx = dx/dx(y) + dy/dx(x).

Thanks.

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# Implicit differentiation and the product rule

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