Use the chain rule to find the partial derivatives

Question

1. Find the equations of the tangent plane and normal line to the surface

x² - 6 y² + z² - xy + 2 yz = 3

at the point P(2, -1,3).

2. Find the linear approximation of the function

f(x,y,z) = √(x² +y² + z²)

at (4,4, 7) and use it to approximate the number √(4.03²+3.98²+6.99²).

3. Use chain rule to find dw/dt with w = ln √xyz and x = cos t, y =sint, z = t².

4. Use the equation

x² sin(y - 2z) = y cos(6zx) + 3

to find ∂z/∂x and ∂z/∂y.

5. Use the Chain rule to find the partial derivatives ∂z/∂s and ∂z/∂t ,if z = e^r cos θ, r = st, θ = √(s²+t²).