What is the derivative of y=(2x)/(1-cot(x)) ?

The derivative of y=(2x)/(1-cot(x)) is (2(1-cot(x)-xcsc^2(x)))/((1-cot(x))^2)

What is the first derivative of y=(2x)/(1-cot(x)) ?

The first derivative of y=(2x)/(1-cot(x)) is (2(1-cot(x)-xcsc^2(x)))/((1-cot(x))^2)

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derivative of

y = \frac{2 x}{1 - cot ( x )}

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

Solution steps

\frac{d}{d x} (\frac{2 x}{1 - cot ( x )})

Take the constant out:

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

= 2 \frac{d}{d x} (\frac{x}{1 - 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} ( 1 - cot ( x ) ) - \frac{d}{d x} ( 1 - cot ( x ) ) x}{( 1 - cot ( x ) ) ^{2}}

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

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

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

Simplify

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

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

\frac{\partial}{\partial x} (3 e^{x y + 9})

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

x \frac{d y}{d x} = y + x^{2} - y^{2}

x \to - 6 lim (2 x + 3)

y = (2 x^{4} + 7)^{2}

What is the derivative of y=(2x)/(1-cot(x)) ?
The derivative of y=(2x)/(1-cot(x)) is (2(1-cot(x)-xcsc^2(x)))/((1-cot(x))^2)
What is the first derivative of y=(2x)/(1-cot(x)) ?
The first derivative of y=(2x)/(1-cot(x)) is (2(1-cot(x)-xcsc^2(x)))/((1-cot(x))^2)