What is the derivative of-4cot(xcsc(x)) ?

The derivative of-4cot(xcsc(x)) is -4(csc(x)-2csc^3(x))

What is the first derivative of-4cot(xcsc(x)) ?

The first derivative of-4cot(xcsc(x)) is -4(csc(x)-2csc^3(x))

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

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

Solution steps

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

Take the constant out:

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

= - 4 \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)

= - 4 (\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)

= - 4 ((- csc^{2} (x)) csc (x) + (- cot (x) csc (x)) cot (x))

Simplify

- 4 ((- csc^{2} (x)) csc (x) + (- cot (x) csc (x)) cot (x)) : - 4 (csc (x) - 2 csc^{3} (x))

= - 4 (csc (x) - 2 csc^{3} (x))

\int - \frac{sin ( 8 x )}{8} d x

\int_{1}^{2} \frac{1}{4 x - x ^{2}} d x

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7 + 6 sin (x^{2})

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What is the derivative of-4cot(xcsc(x)) ?
The derivative of-4cot(xcsc(x)) is -4(csc(x)-2csc^3(x))
What is the first derivative of-4cot(xcsc(x)) ?
The first derivative of-4cot(xcsc(x)) is -4(csc(x)-2csc^3(x))