Solution Found!
Implicit differentiation with three variables Use the
Chapter 11, Problem 46E(choose chapter or problem)
Implicit differentiation with three variables Use the result of Exercise 44 to evaluate \(\frac{\partial z}{\partial x} \text { and } \frac{\partial z}{\partial y^{2}}\) for the following relations.
\(x^{2}+2 y^{2}-3 z^{2}=1\)
Questions & Answers
QUESTION:
Implicit differentiation with three variables Use the result of Exercise 44 to evaluate \(\frac{\partial z}{\partial x} \text { and } \frac{\partial z}{\partial y^{2}}\) for the following relations.
\(x^{2}+2 y^{2}-3 z^{2}=1\)
ANSWER:Solution 46E
Step 1 of 3:
In this problem we need to find the value of by using the implicit differentiation.
Implicit differentiation : Let F be differentiable on its domain and suppose that
Defines z as a differentiable function on x and y , provided
That is , and
, provided
.
Here denotes partial derivative of F with respect to x
denotes partial derivative of F with respect to y
And denotes partial derivative of F with respect to z.
Step 2 of 3:
Given equation is :
Let us consider ,