What is the derivative of sec(xcsc(x)) ?

The derivative of sec(xcsc(x)) is -4cot(2x)csc(2x)

What is the first derivative of sec(xcsc(x)) ?

The first derivative of sec(xcsc(x)) is -4cot(2x)csc(2x)

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\frac{d}{d x} (sec (x) csc (x))

- 4 cot (2 x) csc (2 x)

Solution steps

\frac{d}{d x} (sec (x) csc (x))

Simplify

sec (x) csc (x) : 2 csc (2 x)

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

Take the constant out:

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

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

Apply the chain rule:

- cot (2 x) csc (2 x) \frac{d}{d x} (2 x)

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

\frac{d}{d x} (2 x) = 2

= 2 (- cot (2 x) csc (2 x) \cdot 2)

Simplify

= - 4 cot (2 x) csc (2 x)

What is the derivative of sec(xcsc(x)) ?
The derivative of sec(xcsc(x)) is -4cot(2x)csc(2x)
What is the first derivative of sec(xcsc(x)) ?
The first derivative of sec(xcsc(x)) is -4cot(2x)csc(2x)