What is the derivative of f(x)=((x+2))/((x+4)) ?

The derivative of f(x)=((x+2))/((x+4)) is 2/((x+4)^2)

What is the first derivative of f(x)=((x+2))/((x+4)) ?

The first derivative of f(x)=((x+2))/((x+4)) is 2/((x+4)^2)

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derivative of

f (x) = \frac{( x + 2 )}{( x + 4 )}

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

Solution steps

\frac{d}{d x} (\frac{x + 2}{x + 4})

Apply the Quotient Rule:

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

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

\frac{d}{d x} (x + 2) = 1

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

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

Simplify

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

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

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

\frac{d}{d x} (3 x^{2} - 8 x)

\frac{d y}{d x}, 2 x y = 0

\frac{d}{d x} (\frac{π ^{2}}{x ^{2} + 4 x})

3 x y + x^{2} + y^{2}

What is the derivative of f(x)=((x+2))/((x+4)) ?
The derivative of f(x)=((x+2))/((x+4)) is 2/((x+4)^2)
What is the first derivative of f(x)=((x+2))/((x+4)) ?
The first derivative of f(x)=((x+2))/((x+4)) is 2/((x+4)^2)