What is the derivative of f(x)=3csc(4x) ?

The derivative of f(x)=3csc(4x) is -12cot(4x)csc(4x)

What is the first derivative of f(x)=3csc(4x) ?

The first derivative of f(x)=3csc(4x) is -12cot(4x)csc(4x)

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derivative of

f (x) = 3 csc (4 x)

- 12 cot (4 x) csc (4 x)

Solution steps

\frac{d}{d x} (3 csc (4 x))

Take the constant out:

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

= 3 \frac{d}{d x} (csc (4 x))

Apply the chain rule:

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

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

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

= 3 (- cot (4 x) csc (4 x) \cdot 4)

Simplify

= - 12 cot (4 x) csc (4 x)

What is the derivative of f(x)=3csc(4x) ?
The derivative of f(x)=3csc(4x) is -12cot(4x)csc(4x)
What is the first derivative of f(x)=3csc(4x) ?
The first derivative of f(x)=3csc(4x) is -12cot(4x)csc(4x)