What is the derivative of (2x/(x+8)) ?

The derivative of (2x/(x+8)) is (16)/((x+8)^2)

What is the first derivative of (2x/(x+8)) ?

The first derivative of (2x/(x+8)) is (16)/((x+8)^2)

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\frac{d}{d x} (\frac{2 x}{x + 8})

\frac{16}{( x + 8 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{2 x}{x + 8})

Take the constant out:

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

= 2 \frac{d}{d x} (\frac{x}{x + 8})

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

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

\frac{d}{d x} (x + 8) = 1

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

Simplify

2 \cdot \frac{1 \cdot ( x + 8 ) - 1 \cdot x}{( x + 8 ) ^{2}} : \frac{16}{( x + 8 ) ^{2}}

= \frac{16}{( x + 8 ) ^{2}}

y = 5 csc (x) + 6 cos (x)

y = sin (x), y = 5 x, x = \frac{π}{2}, x = π

\int \frac{1}{2 x + 3 + x} d x

x d y + (y - 3 x y) d x = 0

n = 1 \sum \infty \frac{ln ( n )}{5 n}

What is the derivative of (2x/(x+8)) ?
The derivative of (2x/(x+8)) is (16)/((x+8)^2)
What is the first derivative of (2x/(x+8)) ?
The first derivative of (2x/(x+8)) is (16)/((x+8)^2)