What is the derivative of 4cot(x/7) ?

The derivative of 4cot(x/7) is -4/7 csc^2(x/7)

What is the first derivative of 4cot(x/7) ?

The first derivative of 4cot(x/7) is -4/7 csc^2(x/7)

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derivative of

4 cot (\frac{x}{7})

- \frac{4}{7} csc^{2} (\frac{x}{7})

Solution steps

\frac{d}{d x} (4 cot (\frac{x}{7}))

Take the constant out:

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

= 4 \frac{d}{d x} (cot (\frac{x}{7}))

Apply the chain rule:

- csc^{2} (\frac{x}{7}) \frac{d}{d x} (\frac{x}{7})

= - csc^{2} (\frac{x}{7}) \frac{d}{d x} (\frac{x}{7})

\frac{d}{d x} (\frac{x}{7}) = \frac{1}{7}

= 4 (- csc^{2} (\frac{x}{7}) \frac{1}{7})

Simplify

4 (- csc^{2} (\frac{x}{7}) \frac{1}{7}) : - \frac{4}{7} csc^{2} (\frac{x}{7})

= - \frac{4}{7} csc^{2} (\frac{x}{7})

\frac{d}{d x} ((8 (2 x)^{4} + 5)^{3})

2 x^{3} - 3 x^{2} + 5

x^{^{'}} = 2 x

\frac{d y}{d t} - y = 2 cos (k t), y (0) = 7

\frac{d y}{d t} = \frac{( 4 t + y )}{4 y - t}

What is the derivative of 4cot(x/7) ?
The derivative of 4cot(x/7) is -4/7 csc^2(x/7)
What is the first derivative of 4cot(x/7) ?
The first derivative of 4cot(x/7) is -4/7 csc^2(x/7)