Basic Mathematics05 marksNumerical: second order partial derivativesSecond order partial derivatives
Find the second order derivative fracpartial2 fpartial x2, fracpartial2 fpartial y2, fracpartial2 fpartial xpartial y, fracpartial2 fpartial ypartial x of f(x,y) = x cos y + yex
Find the second order derivative $\frac{\partial^2 f}{\partial x^2}, \frac{\partial^2 f}{\partial y^2}, \frac{\partial^2 f}{\partial x\partial y}, \frac{\partial^2 f}{\partial y\partial x}$ of $f(x,y) = x \cos y + ye^x$ [5]
$$f(x,y) = x\cos y + ye^x$$ Required: $\dfrac{\partial^2 f}{\partial x^2}, \dfrac{\partial^2 f}{\partial y^2}, \dfrac{\partial^2 f}{\partial x,\partial y}, \dfrac{\partial^2 f}{\partial y,\partial x}$ Differentiate with respect to $x$ (treat $y$ constant): $$\frac{\partial f}{\partial x} = \cos...