# Math Help - Derivatives

1. ## Derivatives

Suppose that we have two functions, f(x) and g (x), and that
• f (3) = 4,
• g (3) = 5,
• f '(3) = -4, and
• g '(3) = 5.
Calculate the values of the following derivatives when x is equal to 3.

2. Hello,

Use the quotient rule..

But I don't see any g function here oO

So the derivative of f(x)/x : [x*f'(x)-f(x)]/x^2

Since f(3) is known, f'(3) is known and x=3, you can easily calculate it

3. Hello, Merdiemae!

Suppose that we have a function, $f(x)$, and that: . $f(3) = 4,\;\;f'(3) = \text{-}4$

Calculate the value of $\frac{d}{dx}\left(\frac{f(x)}{x}\right)$ when $x = 3$
We need the Quotient Rule . . .

. . $\frac{d}{dx}\left(\frac{f(x)}{x}\right) \;=\;\frac{x\!\cdot\!f'(x) - 1\!\cdot\!f(x)}{x^2}$

Then: . $\frac{d}{dx}\left(\frac{f(x)}{x}\right)\bigg]_{x=3} \;=\; \frac{3\!\cdot\!f'(3) - 1\!\cdot\!f(3)}{3^2} \;=\;\frac{3(\text{-}4) - 1(4)}{3^2} \;=\;\boxed{-\frac{16}{9}}$