What is the derivative of 3/(sin(x)) ?

The derivative of 3/(sin(x)) is -3cot(x)csc(x)

What is the first derivative of 3/(sin(x)) ?

The first derivative of 3/(sin(x)) is -3cot(x)csc(x)

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\frac{d}{d x} (\frac{3}{sin ( x )})

- 3 cot (x) csc (x)

Solution steps

\frac{d}{d x} (\frac{3}{sin ( x )})

Simplify

\frac{3}{sin ( x )} : 3 csc (x)

= \frac{d}{d x} (3 csc (x))

Take the constant out:

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

= 3 \frac{d}{d x} (csc (x))

Apply the common derivative:

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

= 3 (- cot (x) csc (x))

Simplify

= - 3 cot (x) csc (x)

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