Questions from General Calculus

Q: Explain how to find a first partial derivative of a function of

Explain how to find a first partial derivative of a function of two variables.

Q: Explain how to find a second partial derivative of a function of

Explain how to find a second partial derivative of a function of two variables.

Q: What expression involving a partial derivative gives an approximation to f (

What expression involving a partial derivative gives an approximation to f (a + h, b) - f (a, b)?

Q: Let f (x, y) = 3x2 + xy +

Let f (x, y) = 3x2 + xy + 5y2. Find ∂f/∂x and ∂f/∂y.

Q: Let f (x, y) = 3x – ½ y4

Let f (x, y) = 3x – ½ y4 + 1. Find ∂f/∂x and ∂f/∂y.

Q: Let f (x, y) = ex/y.

Let f (x, y) = ex/y. Find ∂f/∂x and ∂f/∂y.

Q: Let f (x, y) = x/(x -

Let f (x, y) = x/(x - 2y). Find ∂f/∂x and ∂f/∂y.

Q: Let g (x, y) = √(x2 + 2y2

Let g (x, y) = √(x2 + 2y2). Compute g (1, 1), g (0,-1), and g (a, b).

Q: Find a function f (x, y) that has the

Find a function f (x, y) that has the curve y = 2/x2 as a level curve.

Q: Let f (x, y, z) = x3 -

Let f (x, y, z) = x3 - yz2. Find ∂f/∂x, ∂f/∂y and ∂f/∂z.