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

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

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

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

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

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

Solution steps

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

\frac{d}{d x} (cos (x)) = - sin (x)

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

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

Simplify

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

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

\int_{0}^{\frac{π}{4}} sin (3 x) d x

\frac{d}{d x} (\frac{2 ( - x ^{2} - 4 )}{( x ^{2} - 4 ) ^{2}})

\frac{d}{d x} (\frac{( x ^{2} - 2 x )}{x})

x \to 0 lim (\frac{tan ( 4 x )}{3 x})

x \to 2 lim ((3 x + 4)^{5})

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