Find partial derivative of z with respect to the partial of y using the result of the chain rule. ln(x^2+y^2)+xln(z)−cos(xyz)=3.

Alexus Deleon 2022-09-15 Answered
Find partial derivative of z with respect to the partial of y using the result of the chain rule.
ln ( x 2 + y 2 ) + x ln ( z ) cos ( x y z ) = 3.
I would use regular implicit differentiation for this problem but what does "using result of the chain rule" mean?
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Answers (1)

Adelaide Barr
Answered 2022-09-16 Author has 9 answers
The two methods are the same. Notice that implicit differentiation is the chain rule:
y ( f ( x , y , z ( x , y ) ) ) = 0 f y ( x , y , z ( x , y ) ) + z y ( x , y ) f z ( x , y , z ( x , y ) ) = 0
z y = f y f z

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