- #1
Darkmisc
- 204
- 27
An example of implicit differentation in Stewart, 6th ed, p 883, is given as follows:
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.
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.