What is the derivative of f(x)=(6x+16)/(x+3) ?

The derivative of f(x)=(6x+16)/(x+3) is 2/((x+3)^2)

What is the first derivative of f(x)=(6x+16)/(x+3) ?

The first derivative of f(x)=(6x+16)/(x+3) is 2/((x+3)^2)

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derivative of

f (x) = \frac{6 x + 16}{x + 3}

\frac{2}{( x + 3 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{6 x + 16}{x + 3})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( 6 x + 16 ) ( x + 3 ) - \frac{d}{d x} ( x + 3 ) ( 6 x + 16 )}{( x + 3 ) ^{2}}

\frac{d}{d x} (6 x + 16) = 6

\frac{d}{d x} (x + 3) = 1

= \frac{6 ( x + 3 ) - 1 \cdot ( 6 x + 16 )}{( x + 3 ) ^{2}}

Simplify

\frac{6 ( x + 3 ) - 1 \cdot ( 6 x + 16 )}{( x + 3 ) ^{2}} : \frac{2}{( x + 3 ) ^{2}}

= \frac{2}{( x + 3 ) ^{2}}

What is the derivative of f(x)=(6x+16)/(x+3) ?
The derivative of f(x)=(6x+16)/(x+3) is 2/((x+3)^2)
What is the first derivative of f(x)=(6x+16)/(x+3) ?
The first derivative of f(x)=(6x+16)/(x+3) is 2/((x+3)^2)