Find the derivatives of the following functions (1-3) at any point of their domains :
`y=(ax+b)/c, c ne 0`

Answer

To find the derivative of the function \( y = \frac{ax + b}{c} \) where \( c \neq 0 \), we can follow these steps:

### Step 1: Rewrite the Function
We can rewrite the function in a simpler form:
\[ y = \frac{ax}{c} + \frac{b}{c} \]

### Step 2: Identify the Constants
From the rewritten function, we can identify the constants:
- The coefficient of \( x \) is \( \frac{a}{c} \).
- The constant term is \( \frac{b}{c} \).

### Step 3: Differentiate the Function
Now, we differentiate the function with respect to \( x \):
- The derivative of \( \frac{ax}{c} \) is \( \frac{a}{c} \) (since the derivative of \( x \) is 1).
- The derivative of the constant \( \frac{b}{c} \) is 0.

Thus, the derivative \( y' \) is:
\[ y' = \frac{a}{c} + 0 = \frac{a}{c} \]

### Final Answer
Therefore, the derivative of the function \( y = \frac{ax + b}{c} \) is:
\[ y' = \frac{a}{c} \]

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