Question

Use the definition of the derivative to calculate the derivative of f)x)=7/(x+6)

Answer 1

Hello !

Answer:

`\Large \boxed{\sf f'(x)=-(7)/((x+6)^2) }`

Explanation:

Let's remember !

• The derivate of
  `\sf (u(x))/(v(x))` is
  `\sf (u'(x)v(x)-u(x)v'(x))/(v(x))^2`
• The derivate of
  `\sf \lambda x` if
  `\lambda` (where
  `\lambda` is a real number)
• The derivate of
  `k` is 0 (where k is a constant)

Given :
`\sf f(x) = (7)/(x+6)`

We have :

• 
  `\sf u(x) =7`
• 
  `\sf v(x)=x+6`

Let's derivate u and v with the previous formulas:

• 
  `\sf u'(x)=0`
• 
  `\sf v'(x)=1`

Now we can apply the first formula !

`\sf f'(x)=(0*(x+6)-7*1)/((x+6)^2) \\\boxed{\sf f'(x)=-(7)/((x+6)^2) }`

Have a nice day ;)