If f(x,y) = x3 + x2y3 - 2y2, find fx(2,1) and fy(2,1). | Mathematics I 2080

Mathematics I20805 marksNumerical: partial derivativesPartial derivatives

If $f(x,y) = x^3 + x^2y^3 - 2y^2$ , find $f_x(2,1)$ and $f_y(2,1)$ . [5]

If $f(x,y) = x^3 + x^2y^3 - 2y^2$, find $f_x(2,1)$ and $f_y(2,1)$. [5]

$f(x, y) = x^3 + x^2y^3 - 2y^2$ Required: $fx(2,1)$ and $fy(2,1)$ . --- Differentiate with respect to $x$ , treating $y$ as constant: - $\frac{\partial}{\partial x}(x^3) = 3x^2$ - $\frac{\partial}{\partial x}(x^2 y^3) = 2x y^3$ - $\frac{\partial}{\partial x}(-2y^2) = 0$ $fx(x,y) = 3x^2 + 2xy^3$ ...

$$f(x, y) = x^3 + x^2y^3 - 2y^2$$ Required: $fx(2,1)$ and $fy(2,1)$. --- Differentiate with respect to $x$, treating $y$ as constant: - $\frac{\partial}{\partial x}(x^3) = 3x^2$ - $\frac{\partial}{\partial x}(x^2 y^3) = 2x y^3$ - $\frac{\partial}{\partial x}(-2y^2) = 0$ $$fx(x,y) = 3x^2 + 2xy^3$$...

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