Find the partial derivatives fx, fy and fxy of f(x,y) = sqrtx y3 + x4 | Basic Mathematics 2081

Basic Mathematics20815 marksNumerical: partial derivativesPartial derivatives

Find the partial derivatives $f_x$ , $f_y$ and $f_{xy}$ of $f(x,y) = \sqrt{x} y^3 + x^4 y$ at $(-4,1)$ . [5]

Find the partial derivatives $f_x$, $f_y$ and $f_{xy}$ of $f(x,y) = \sqrt{x} y^3 + x^4 y$ at $(-4,1)$. [5]

Function: $f(x,y) = \sqrt{x}\, y^3 + x^4 y$ - Evaluation point: $(-4, 1)$ --- Treat $y$ as constant. Write $\sqrt{x} = x^{1/2}$ . $fx = \frac{1}{2}x^{-1/2}\,y^3 + 4x^3 y = \frac{y^3}{2\sqrt{x}} + 4x^3 y$ --- Treat $x$ as constant. $fy = 3\sqrt{x}\,y^2 + x^4$ --- Differentiate $fx$ with respe...

Function: $f(x,y) = \sqrt{x}, y^3 + x^4 y$ - Evaluation point: $(-4, 1)$ --- Treat $y$ as constant. Write $\sqrt{x} = x^{1/2}$. $$fx = \frac{1}{2}x^{-1/2},y^3 + 4x^3 y = \frac{y^3}{2\sqrt{x}} + 4x^3 y$$ --- Treat $x$ as constant. $$fy = 3\sqrt{x},y^2 + x^4$$ --- Differentiate $fx$ with respe...

Find the partial derivatives fx, fy and fxy of f(x,y) = sqrtx y3 + x4 y at (-4,1).