What is the derivative of (4x)/(9-cot(x)) ?

The derivative of (4x)/(9-cot(x)) is (4(9-cot(x)-xcsc^2(x)))/((9-cot(x))^2)

What is the first derivative of (4x)/(9-cot(x)) ?

The first derivative of (4x)/(9-cot(x)) is (4(9-cot(x)-xcsc^2(x)))/((9-cot(x))^2)

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derivative

\frac{4 ( 9 - cot ( x ) - x csc ^{2} ( x ) )}{( 9 - cot ( x ) ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{4 x}{9 - cot ( x )})

Take the constant out:

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

= 4 \frac{d}{d x} (\frac{x}{9 - cot ( x )})

Apply the Quotient Rule:

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

= 4 \cdot \frac{\frac{d x}{d x} ( 9 - cot ( x ) ) - \frac{d}{d x} ( 9 - cot ( x ) ) x}{( 9 - cot ( x ) ) ^{2}}

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

\frac{d}{d x} (9 - cot (x)) = csc^{2} (x)

= 4 \cdot \frac{1 \cdot ( 9 - cot ( x ) ) - csc ^{2} ( x ) x}{( 9 - cot ( x ) ) ^{2}}

Simplify

4 \cdot \frac{1 \cdot ( 9 - cot ( x ) ) - csc ^{2} ( x ) x}{( 9 - cot ( x ) ) ^{2}} : \frac{4 ( 9 - cot ( x ) - x csc ^{2} ( x ) )}{( 9 - cot ( x ) ) ^{2}}

= \frac{4 ( 9 - cot ( x ) - x csc ^{2} ( x ) )}{( 9 - cot ( x ) ) ^{2}}

What is the derivative of (4x)/(9-cot(x)) ?
The derivative of (4x)/(9-cot(x)) is (4(9-cot(x)-xcsc^2(x)))/((9-cot(x))^2)
What is the first derivative of (4x)/(9-cot(x)) ?
The first derivative of (4x)/(9-cot(x)) is (4(9-cot(x)-xcsc^2(x)))/((9-cot(x))^2)