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

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

\int ln (x - 1) d x

\int \frac{1}{x ^{2} 81 x ^{2} - 49} d x

\frac{d}{d x} (4 x^{π})

\frac{d}{d x} (3 cos^{3} (x))

\frac{d}{d x} ((1 + cos (x))^{8})

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