Total differential

Exercise

1.

Find the total differential and gradient．Find also the tangent plane and the normal line corresponding to $(1,1)$.

(a)

$${f(x,y) = x^3 y^4}$$

(b)

$${f(x,y) = x^3 y + x^2 y^4}$$

(c)

$${z = x^2 y e^{2x}}$$

2.

Apporoximate the followings using the total differential.．

(a)

$${\sqrt{125}\sqrt[4]{17}}$$

(b)

$${\sin{(\frac{6\pi}{7})}\cos{(\frac{\pi}{3})}}$$