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

The derivative of (8x/(5-cot(x))) is (8(5-cot(x)-xcsc^2(x)))/((5-cot(x))^2)

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

The first derivative of (8x/(5-cot(x))) is (8(5-cot(x)-xcsc^2(x)))/((5-cot(x))^2)

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\frac{d}{d x} (\frac{8 x}{5 - cot ( x )})

\frac{8 ( 5 - cot ( x ) - x csc ^{2} ( x ) )}{( 5 - cot ( x ) ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{8 x}{5 - cot ( x )})

Take the constant out:

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

= 8 \frac{d}{d x} (\frac{x}{5 - cot ( x )})

Apply the Quotient Rule:

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

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

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

\frac{d}{d x} (5 - cot (x)) = csc^{2} (x)

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

Simplify

8 \cdot \frac{1 \cdot ( 5 - cot ( x ) ) - csc ^{2} ( x ) x}{( 5 - cot ( x ) ) ^{2}} : \frac{8 ( 5 - cot ( x ) - x csc ^{2} ( x ) )}{( 5 - cot ( x ) ) ^{2}}

= \frac{8 ( 5 - cot ( x ) - x csc ^{2} ( x ) )}{( 5 - cot ( x ) ) ^{2}}

What is the derivative of (8x/(5-cot(x))) ?
The derivative of (8x/(5-cot(x))) is (8(5-cot(x)-xcsc^2(x)))/((5-cot(x))^2)
What is the first derivative of (8x/(5-cot(x))) ?
The first derivative of (8x/(5-cot(x))) is (8(5-cot(x)-xcsc^2(x)))/((5-cot(x))^2)