What is the derivative of (2x/(x+7)) ?

The derivative of (2x/(x+7)) is (14)/((x+7)^2)

What is the first derivative of (2x/(x+7)) ?

The first derivative of (2x/(x+7)) is (14)/((x+7)^2)

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\frac{d}{d x} (\frac{2 x}{x + 7})

\frac{14}{( x + 7 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{2 x}{x + 7})

Take the constant out:

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

= 2 \frac{d}{d x} (\frac{x}{x + 7})

Apply the Quotient Rule:

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

= 2 \cdot \frac{\frac{d x}{d x} ( x + 7 ) - \frac{d}{d x} ( x + 7 ) x}{( x + 7 ) ^{2}}

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

\frac{d}{d x} (x + 7) = 1

= 2 \cdot \frac{1 \cdot ( x + 7 ) - 1 \cdot x}{( x + 7 ) ^{2}}

Simplify

2 \cdot \frac{1 \cdot ( x + 7 ) - 1 \cdot x}{( x + 7 ) ^{2}} : \frac{14}{( x + 7 ) ^{2}}

= \frac{14}{( x + 7 ) ^{2}}

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

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

\int_{0}^{2} (y - 1) (2 y + 1) d y

- 6 y^{^{''}} + 24 y = 0, y (- 1) = 1, y^{^{'}} (1) = 1

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

What is the derivative of (2x/(x+7)) ?
The derivative of (2x/(x+7)) is (14)/((x+7)^2)
What is the first derivative of (2x/(x+7)) ?
The first derivative of (2x/(x+7)) is (14)/((x+7)^2)