What is the derivative of 1/2 csc(x/4) ?

The derivative of 1/2 csc(x/4) is -1/8 cot(x/4)csc(x/4)

What is the first derivative of 1/2 csc(x/4) ?

The first derivative of 1/2 csc(x/4) is -1/8 cot(x/4)csc(x/4)

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\frac{d}{d x} (\frac{1}{2} csc (\frac{x}{4}))

- \frac{1}{8} cot (\frac{x}{4}) csc (\frac{x}{4})

Solution steps

\frac{d}{d x} (\frac{1}{2} csc (\frac{x}{4}))

Take the constant out:

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

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

Apply the chain rule:

- cot (\frac{x}{4}) csc (\frac{x}{4}) \frac{d}{d x} (\frac{x}{4})

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

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

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

Simplify

\frac{1}{2} (- cot (\frac{x}{4}) csc (\frac{x}{4}) \frac{1}{4}) : - \frac{1}{8} cot (\frac{x}{4}) csc (\frac{x}{4})

= - \frac{1}{8} cot (\frac{x}{4}) csc (\frac{x}{4})

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

ln (x^{2} + 1) + e^{- x^{2}}

\frac{100}{x}

\int \frac{x ^{2}}{( x + 1 ) ^{3}} d x

5 y

What is the derivative of 1/2 csc(x/4) ?
The derivative of 1/2 csc(x/4) is -1/8 cot(x/4)csc(x/4)
What is the first derivative of 1/2 csc(x/4) ?
The first derivative of 1/2 csc(x/4) is -1/8 cot(x/4)csc(x/4)