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

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

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

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

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\frac{d}{d x} (x + cot (\frac{x}{2}))

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

Solution steps

\frac{d}{d x} (x + cot (\frac{x}{2}))

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

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

\frac{\partial}{\partial y} (10 x y e^{- x^{2} - y^{2}})

\frac{d}{d x} (- 3 cot (1 - x^{2}))

x \to 0 lim (3 - \frac{1}{x})

f (x) = π^{x}

\frac{d}{d x} (x x^{2} - 3 x + 2)

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