 Derivatives

 Solutions

Find the derivative of f(x) = 8

The derivative of a constant is 0. Therefore:

```f(x)  = 8

f'(x) = 0```

Find the derivative of f(x) = 6x

For a function of the form f(x) = ax, the derivative is f'(x) = a. Therefore:

```f(x) = 6x

f'(x) = 6```

Find the derivative of f(x) = 3x + 7

Knowing that for a function f(x) = ax + b, its derivative is f'(x) = a, we have

```f(x) = 3x + 7

f'(x) = 3```

Find the derivative of f(x) = 8 - 5x

We know if a function has the form f(x) = ax + b, the derivative is f'(x) = a.

Let's re-write the function as

```f(x) = 8 - 5x
= -5x + 8

f'(x) = -5```

Find the derivative of f(x) = 3(7x + 4)

To convert the function to the form ax + b, we can write it as:

```f(x) = 3 * 7x + 3 * 4
= 21x + 12```

For a function of the form f(x) = ax + b, the derivative is f'(x) = a.

```f(x)  = 21x + 12

f'(x) = 21```
 Find the derivative of We can first simplify the function as follows:

 `f(x) = ` ` =` ` =` `2x - 3`

We can then calculate the derivative knowing that, for a function of the form f(x) = ax + b, the derivative is f'(x) = a. Therefore:

```f(x)  = 2x - 3

f'(x) = 2```