Exercise · ZW-SMOOTH-FUNCTION-010 · ★★☆ Intermediate
Let \(f(x,y)=x^{2}y+\sin y\). What is \(\dfrac{\partial^{2} f}{\partial x\,\partial y}\)?
Choose one option.
Show answer
- A. \(2x\)
Explanation
Differentiating first with respect to \(y\) gives \(x^{2}+\cos y\), and then with respect to \(x\) gives \(2x\).
Review the concept: Smooth function
A smooth function is a function between spaces with differentiable structure that, written in local coordinates, has derivatives of all orders.
\[f\in C^{\infty}(M,N)\]
More practice problems: smooth function
- ZW-SMOOTH-FUNCTION-001 What does it mean for f to be of class C^∞?
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- ZW-SMOOTH-FUNCTION-006 Let f(x)=x^2 if x≥ 0 and f(x)=0 if x<0. Is f smooth?
- ZW-SMOOTH-FUNCTION-007 If f and g from ℝ to ℝ are smooth, what can be said about g∘ f?
- ZW-SMOOTH-FUNCTION-008 Let f(x)=x^2sin (1/x) for xne 0 and f(0)=0. Which statement is correct?