Find the second-order partial derivatives of the function. Show that the mixed partial derivatives $f_{xy}$ and $f_{yx}$ are equal.\ $f(x, y) = \ln(3 + x^2y^2)$ $f_{xx} = $ $f_{yy} = $ $f_{xy} = $ $f_{yx} = $
Added by Jonathan H.
Close
Step 1
∂f/∂x = y^1*n*(3+x^2) + x*y^1*n*(2x) = y^1*n*(3+x^2) + 2x^2*y^1*n ∂f/∂y = x*y^1*n*(1) + x^2*y^1*n*(1) = x*y^1*n + x^2*y^1*n Now, let's find the second-order partial derivatives. ∂²f/∂x² = 2y^1*n + 4xy^1*n ∂²f/∂y² = x^2*n Show more…
Show all steps
Your feedback will help us improve your experience
Ishana K and 96 other Calculus 1 / AB educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Find the second-order partial derivatives of the function. In each case, show that the mixed partial derivatives $f_{x y}$ and $f_{y x}$ are equal. $$f(x, y)=x^{3}+x^{2} y^{2}+y^{3}+x+y$$
Calculus of Several Variables
Partial Derivative
Find the second-order partial derivatives of the function. In each case, show that the mixed partial derivatives $f_{x y}$ and $f_{y x}$ are equal. $$f(x, y)=x^{2} y+x y^{3}$$
Find the second-order partial derivatives of the function. In each case, show that the mixed partial derivatives $f_{x y}$ and $f_{y x}$ are equal. $$f(x, y)=x^{3}+x^{2} y+x+4$$
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
Watch the video solution with this free unlock.
EMAIL
PASSWORD