Find the partial derivatives of f(x, y) = x2 + 2x3y2 - 3y2 + x + y at | Mathematics I 2078

Mathematics I20785 marksNumerical: partial derivativesPartial derivatives

Find the partial derivatives of $f(x, y) = x^2 + 2x^3y^2 - 3y^2 + x + y$ at (1,2). [5]

Function: $f(x, y) = x^2 + 2x^3y^2 - 3y^2 + x + y$ Point of evaluation: $(x, y) = (1, 2)$ Required: $\dfrac{\partial f}{\partial x}$ and $\dfrac{\partial f}{\partial y}$ at $(1, 2)$ . --- Treat $y$ as constant: $\frac{\partial f}{\partial x} = 2x + 2(3x^2)y^2 - 0 + 1 + 0$ $$\boxed{\frac{\partial...

Function: $f(x, y) = x^2 + 2x^3y^2 - 3y^2 + x + y$ Point of evaluation: $(x, y) = (1, 2)$ Required: $\dfrac{\partial f}{\partial x}$ and $\dfrac{\partial f}{\partial y}$ at $(1, 2)$. --- Treat $y$ as constant: $$\frac{\partial f}{\partial x} = 2x + 2(3x^2)y^2 - 0 + 1 + 0$$ $$\boxed{\frac{\partial...

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Find the partial derivatives of f(x, y) = x2 + 2x3y2 - 3y2 + x + y at (1,2).