What is the derivative of-2cot(xcsc(x)) ?

The derivative of-2cot(xcsc(x)) is -2(csc(x)-2csc^3(x))

What is the first derivative of-2cot(xcsc(x)) ?

The first derivative of-2cot(xcsc(x)) is -2(csc(x)-2csc^3(x))

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

- 2 (csc (x) - 2 csc^{3} (x))

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = cot (x), g = csc (x)

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

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

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

= - 2 ((- csc^{2} (x)) csc (x) + (- cot (x) csc (x)) cot (x))

Simplify

- 2 ((- csc^{2} (x)) csc (x) + (- cot (x) csc (x)) cot (x)) : - 2 (csc (x) - 2 csc^{3} (x))

= - 2 (csc (x) - 2 csc^{3} (x))

2 x^{2} - 5

h (x) = (x - 2) (2 x + 3)

\int 3 - e^{2 x} d x

\frac{d}{d x} (2 ln (2 x^{3}))

x^{2} = e^{(x - y)}

What is the derivative of-2cot(xcsc(x)) ?
The derivative of-2cot(xcsc(x)) is -2(csc(x)-2csc^3(x))
What is the first derivative of-2cot(xcsc(x)) ?
The first derivative of-2cot(xcsc(x)) is -2(csc(x)-2csc^3(x))