What is the derivative of ((x+9))/((x+4)) ?

The derivative of ((x+9))/((x+4)) is -5/((x+4)^2)

What is the first derivative of ((x+9))/((x+4)) ?

The first derivative of ((x+9))/((x+4)) is -5/((x+4)^2)

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derivative of

\frac{( x + 9 )}{( x + 4 )}

- \frac{5}{( x + 4 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x + 9}{x + 4})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x + 9 ) ( x + 4 ) - \frac{d}{d x} ( x + 4 ) ( x + 9 )}{( x + 4 ) ^{2}}

\frac{d}{d x} (x + 9) = 1

\frac{d}{d x} (x + 4) = 1

= \frac{1 \cdot ( x + 4 ) - 1 \cdot ( x + 9 )}{( x + 4 ) ^{2}}

Simplify

\frac{1 \cdot ( x + 4 ) - 1 \cdot ( x + 9 )}{( x + 4 ) ^{2}} : - \frac{5}{( x + 4 ) ^{2}}

= - \frac{5}{( x + 4 ) ^{2}}

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What is the derivative of ((x+9))/((x+4)) ?
The derivative of ((x+9))/((x+4)) is -5/((x+4)^2)
What is the first derivative of ((x+9))/((x+4)) ?
The first derivative of ((x+9))/((x+4)) is -5/((x+4)^2)