Basic Mathematics20775 marksNumerical: directional derivativeDirectional derivatives
Find the derivatives of the function f(x,y) = x3 - xy2 + x2y - y3 at the point p0(5,5) in the direction of vecu = 4veci + 3vecj.
Find the derivatives of the function $f(x,y) = x^3 - xy^2 + x^2y - y^3$ at the point $p_0(5,5)$ in the direction of $\vec{u} = 4\vec{i} + 3\vec{j}$. [5]
- Function: $f(x,y) = x^3 - xy^2 + x^2y - y^3$ - Point: $p0(5,5)$ - Direction: $\vec{u} = 4\vec{i} + 3\vec{j}$ $$D{\vec{u}}f = \nabla f \cdot \hat{u}$$ $$\frac{\partial f}{\partial x} = 3x^2 - y^2 + 2xy$$ $$\frac{\partial f}{\partial y} = -2xy + x^2 - 3y^2$$ $$fx(5,5) = 3(25) - 25 + 2(25) = 75 - ...