What is the derivative of 4cot(1/4 x) ?

The derivative of 4cot(1/4 x) is -csc^2(x/4)

What is the first derivative of 4cot(1/4 x) ?

The first derivative of 4cot(1/4 x) is -csc^2(x/4)

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\frac{d}{d x} (4 cot (\frac{1}{4} x))

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

Solution steps

\frac{d}{d x} (4 cot (\frac{1}{4} x))

Simplify

4 cot (\frac{1}{4} x) : 4 cot (\frac{x}{4})

= \frac{d}{d x} (4 cot (\frac{x}{4}))

Take the constant out:

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

= 4 \frac{d}{d x} (cot (\frac{x}{4}))

Apply the chain rule:

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

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

\frac{d}{d x} (\frac{x}{4}) = \frac{1}{4}

= 4 (- csc^{2} (\frac{x}{4}) \frac{1}{4})

Simplify

4 (- csc^{2} (\frac{x}{4}) \frac{1}{4}) : - csc^{2} (\frac{x}{4})

= - csc^{2} (\frac{x}{4})

What is the derivative of 4cot(1/4 x) ?
The derivative of 4cot(1/4 x) is -csc^2(x/4)
What is the first derivative of 4cot(1/4 x) ?
The first derivative of 4cot(1/4 x) is -csc^2(x/4)