Exercise · ZW-PARTIAL-DERIVATIVE-007 · ★★☆ Intermediate
For \(f(x,y)=x^2y^3\), compute the mixed partial derivative \(f_{xy}=\dfrac{\partial}{\partial y}\left(f_x\right)\).
Choose one option.
Show answer
- A. \(6 x y^{2}\)
Explanation
First \(f_x=2xy^3\), then differentiate with respect to \(y\): \(6xy^2\).
Review the concept: Partial derivative
The partial derivative of a function \(f(x,y)\) with respect to \(x\) at a point \((a,b)\) is the ordinary derivative of the one-variable function obtained by fixing \(y=b\) and letting only \(x\) vary.
\[f_x(a,b)=\lim_{h\to0}\frac{f(a+h,b)-f(a,b)}{h}\]
More practice problems: partial derivative
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- ZW-PARTIAL-DERIVATIVE-009 For f(x,y)=|x|+y, which statement is true at the origin?