What is the derivative of (2000/(sin(3x))) ?

The derivative of (2000/(sin(3x))) is -6000cot(3x)csc(3x)

What is the first derivative of (2000/(sin(3x))) ?

The first derivative of (2000/(sin(3x))) is -6000cot(3x)csc(3x)

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\frac{d}{d x} (\frac{2000}{sin ( 3 x )})

- 6000 cot (3 x) csc (3 x)

Solution steps

\frac{d}{d x} (\frac{2000}{sin ( 3 x )})

Simplify

\frac{2000}{sin ( 3 x )} : 2000 csc (3 x)

= \frac{d}{d x} (2000 csc (3 x))

Take the constant out:

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

= 2000 \frac{d}{d x} (csc (3 x))

Apply the chain rule:

- cot (3 x) csc (3 x) \frac{d}{d x} (3 x)

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

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

= 2000 (- cot (3 x) csc (3 x) \cdot 3)

Simplify

= - 6000 cot (3 x) csc (3 x)

y = \frac{5 + x f ( x )}{x}

y = 1 - x^{2}, y = 2 x, y = \frac{1}{2} x

\int_{0}^{1} e^{3 x} - e^{x} d x

\int \frac{y + 1}{y ^{2} + 2 y - 4} d y

\int 9 x^{4} d x

What is the derivative of (2000/(sin(3x))) ?
The derivative of (2000/(sin(3x))) is -6000cot(3x)csc(3x)
What is the first derivative of (2000/(sin(3x))) ?
The first derivative of (2000/(sin(3x))) is -6000cot(3x)csc(3x)