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Popular >

derivative of 3cot(x/8)

Solution

\frac{d}{d x} (3 cot (\frac{x}{8}))

Solution

- \frac{3}{8} csc^{2} (\frac{x}{8})

Solution steps

\frac{d}{d x} (3 cot (\frac{x}{8}))

Take the constant out:

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

= 3 \frac{d}{d x} (cot (\frac{x}{8}))

Apply the chain rule:

- csc^{2} (\frac{x}{8}) \frac{d}{d x} (\frac{x}{8})

= - csc^{2} (\frac{x}{8}) \frac{d}{d x} (\frac{x}{8})

\frac{d}{d x} (\frac{x}{8}) = \frac{1}{8}

= 3 (- csc^{2} (\frac{x}{8}) \frac{1}{8})

Simplify

3 (- csc^{2} (\frac{x}{8}) \frac{1}{8}) : - \frac{3}{8} csc^{2} (\frac{x}{8})

= - \frac{3}{8} csc^{2} (\frac{x}{8})

Popular Examples

integral of ze^{2z}

\int z e^{2 z} d z

y^{^{''}} = 6 t^{2}

integral from 0 to 6 of x^3sqrt(x^2+36)

\int_{0}^{6} x^{3} x^{2} + 36 d x

limit as x approaches-3-of ((x+2))/(x+3)

x \to - 3 - lim (\frac{( x + 2 )}{x + 3})

x(e^{y/x}-1)y^'=e^{y/x}(y-x),y(1)=0

x (e^{\frac{y}{x}} - 1) y^{^{'}} = e^{\frac{y}{x}} (y - x), y (1) = 0

Frequently Asked Questions (FAQ)

What is the derivative of 3cot(x/8) ?
The derivative of 3cot(x/8) is -3/8 csc^2(x/8)
What is the first derivative of 3cot(x/8) ?
The first derivative of 3cot(x/8) is -3/8 csc^2(x/8)