Total differential

Exercise

1.: Find the total differential and gradient．Find also the tangent plane and the normal line corresponding to .
(a): $\displaystyle{f(x,y) = x^3 y^4}$
(b): $\displaystyle{f(x,y) = x^3 y + x^2 y^4}$
(c): $\displaystyle{z = x^2 y e^{2x}}$
2.: Apporoximate the followings using the total differential.．
(a): $\displaystyle{\sqrt{125}\sqrt[4]{17}}$
(b): $\displaystyle{\sin{(\frac{6\pi}{7})}\cos{(\frac{\pi}{3})}}$