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Calculus of Several Variables Calculator

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Example
Created on 2024-06-20Asked by Evelyn White (Solvelet student)
Find the partial derivatives fx \frac{\partial f}{\partial x} and fy \frac{\partial f}{\partial y} for f(x,y)=x2y+y3 f(x,y) = x^2y + y^3 .

Solution

Step 1: Identify the function f(x,y)=x2y+y3 f(x,y) = x^2y + y^3 . Step 2: Find the partial derivative with respect to x x : fx=x(x2y+y3)=2xy. \frac{\partial f}{\partial x} = \frac{\partial}{\partial x} (x^2y + y^3) = 2xy. Step 3: Find the partial derivative with respect to y y : fy=y(x2y+y3)=x2+3y2. \frac{\partial f}{\partial y} = \frac{\partial}{\partial y} (x^2y + y^3) = x^2 + 3y^2. Step 4: Conclusion. The partial derivatives are fx=2xy \frac{\partial f}{\partial x} = 2xy and fy=x2+3y2 \frac{\partial f}{\partial y} = x^2 + 3y^2 . Solved on Solvelet with Basic AI Model
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