For f(x,y) = e^x sin(xy), find all second partial derivatives fxx, fxy, fyx and fyy.
Added by Ignacio G.
Step 1
fx = ∂f/∂x = e^x sin(xy) + e^x y cos(xy) = e^x (sin(xy) + y cos(xy)) fy = ∂f/∂y = e^x x cos(xy) Now, we can find the second partial derivatives. fxx = ∂^2f/∂x^2 = e^x (sin(xy) + y cos(xy)) + e^x (cos(xy) + y cos(xy) - y^2 sin(xy)) = e^x (2 cos(xy) + y^2 Show more…
Show all steps
Close
Your feedback will help us improve your experience
Ahmet Yavas and 91 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 all the second partial derivatives. f(x, y) = sin^2(mx + ny) fxx(x, y) = fxy(x, y) = fyx(x, y) = fyy(x, y) =
Sri K.
Find all the second partial derivatives f(x, y) = x^4y - 4x^5y^2 fxx(x, y) fxy(x, y) fyx(x, y) fyy(x, y)
Find all first partial derivatives of each function. $$f(x, y)=y \cos \left(x^{2}+y^{2}\right)$$
Derivatives for Functions of Two or More Variables
Partial Derivatives
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD