What is the derivative of (8x/(x+5)) ?

The derivative of (8x/(x+5)) is (40)/((x+5)^2)

What is the first derivative of (8x/(x+5)) ?

The first derivative of (8x/(x+5)) is (40)/((x+5)^2)

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\frac{d}{d x} (\frac{8 x}{x + 5})

\frac{40}{( x + 5 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{8 x}{x + 5})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 8 \frac{d}{d x} (\frac{x}{x + 5})

Apply the Quotient Rule:

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

= 8 \cdot \frac{\frac{d x}{d x} ( x + 5 ) - \frac{d}{d x} ( x + 5 ) x}{( x + 5 ) ^{2}}

\frac{d x}{d x} = 1

\frac{d}{d x} (x + 5) = 1

= 8 \cdot \frac{1 \cdot ( x + 5 ) - 1 \cdot x}{( x + 5 ) ^{2}}

Simplify

8 \cdot \frac{1 \cdot ( x + 5 ) - 1 \cdot x}{( x + 5 ) ^{2}} : \frac{40}{( x + 5 ) ^{2}}

= \frac{40}{( x + 5 ) ^{2}}

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What is the derivative of (8x/(x+5)) ?
The derivative of (8x/(x+5)) is (40)/((x+5)^2)
What is the first derivative of (8x/(x+5)) ?
The first derivative of (8x/(x+5)) is (40)/((x+5)^2)