What is the derivative of the function f(x)=\frac{3x-5}{5x+2}?

Question

What is the derivative of the function

f (x) = \frac{3 x - 5}{5 x + 2}

?

Answer 1

Step 1
The quotient rule states that
if

y = \frac{f (x)}{g (x)}

, then

\frac{d y}{d x} = \frac{f^{'} (x) g (x) - g^{'} (x) f (x)}{{(g (x))}^{2}}

Now if we apply this to the given function

f^{'} (x) = \frac{3 (5 x + 2) - 5 (3 x - 5)}{{(5 x + 2)}^{2}}

f^{'} (x) = \frac{15 x + 6 - 15 x + 25}{{(5 x + 2)}^{2}}

f^{'} (x) = \frac{31}{{(5 x + 2)}^{2}}

Answer 2

Step 1
Quotient Rule:

{(\frac{u}{v})}^{'} = \frac{v u^{'} - u v^{'}}{v^{2}}

{(\frac{u}{v})}^{'} = \frac{(5 x + 2) (3) - (3 x - 5) (5)}{{(5 x + 2)}^{2}}

= \frac{15 x + 6 - (15 x - 25)}{{(5 x + 2)}^{2}}

= \frac{31}{{(5 x + 2)}^{2}}

If you are enrolled in a calculus course, you really need to review these elementary differentiation rules.

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