What is the derivative of (cot(x))/(1+cot(x)) ?

The derivative of (cot(x))/(1+cot(x)) is -(csc^2(x))/((1+cot(x))^2)

What is the first derivative of (cot(x))/(1+cot(x)) ?

The first derivative of (cot(x))/(1+cot(x)) is -(csc^2(x))/((1+cot(x))^2)

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derivative of

\frac{cot ( x )}{1 + cot ( x )}

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

Solution steps

\frac{d}{d x} (\frac{cot ( x )}{1 + cot ( x )})

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

cos^{3} (π x)

x \to 1 + lim (2 x)

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

x \to 2 lim (\frac{( 3 )}{x + 2})

\frac{\partial}{\partial x} (- 7 x y)

What is the derivative of (cot(x))/(1+cot(x)) ?
The derivative of (cot(x))/(1+cot(x)) is -(csc^2(x))/((1+cot(x))^2)
What is the first derivative of (cot(x))/(1+cot(x)) ?
The first derivative of (cot(x))/(1+cot(x)) is -(csc^2(x))/((1+cot(x))^2)