Problem 70 - Essential Calculus

Question

Mentally determine \(d y / d x\). (a) \(x=t, \quad y=4\) (b) \(x=t, \quad y=4 t-3\)

Step-by-Step Solution

Answer

(a) 0 (b) 4

Step 1: Differentiate y=4 for dy/dx

In the first situation, y is constant (y=4). The derivative of any constant is zero. Thus, for part (a), dy/dx equals zero.

Step 2: Differentiate y=4t-3 for dy/dx

In the second situation, y equals 4t minus 3. This is a linear function of t. Remember, the derivative of a variable with respect to itself is 1, and constants disappear upon differentiation. Hence, dy/dx is the derivative of 4t minus 3 with respect to t, which equals 4.