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

The derivative of (2x)/(7-cot(x)) is (2(7-cot(x)-xcsc^2(x)))/((7-cot(x))^2)

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

The first derivative of (2x)/(7-cot(x)) is (2(7-cot(x)-xcsc^2(x)))/((7-cot(x))^2)

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derivative of

\frac{2 x}{7 - cot ( x )}

\frac{2 ( 7 - cot ( x ) - x csc ^{2} ( x ) )}{( 7 - cot ( x ) ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{2 x}{7 - cot ( x )})

Take the constant out:

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

= 2 \frac{d}{d x} (\frac{x}{7 - cot ( x )})

Apply the Quotient Rule:

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

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

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

\frac{d}{d x} (7 - cot (x)) = csc^{2} (x)

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

Simplify

2 \cdot \frac{1 \cdot ( 7 - cot ( x ) ) - csc ^{2} ( x ) x}{( 7 - cot ( x ) ) ^{2}} : \frac{2 ( 7 - cot ( x ) - x csc ^{2} ( x ) )}{( 7 - cot ( x ) ) ^{2}}

= \frac{2 ( 7 - cot ( x ) - x csc ^{2} ( x ) )}{( 7 - cot ( x ) ) ^{2}}

\int y (y^{2} + 1)^{5} d y

x \to - 6 lim (\frac{( x + 7 )}{x + 6})

\int \frac{6 e ^{2 x}}{e ^{2 x} + 12 e ^{x} + 27} d x

\int x (x^{2} + x) d x

2 z (3 z + 1) d w + (1 - 2 w) d z = 0

What is the derivative of (2x)/(7-cot(x)) ?
The derivative of (2x)/(7-cot(x)) is (2(7-cot(x)-xcsc^2(x)))/((7-cot(x))^2)
What is the first derivative of (2x)/(7-cot(x)) ?
The first derivative of (2x)/(7-cot(x)) is (2(7-cot(x)-xcsc^2(x)))/((7-cot(x))^2)