What is the derivative of-6cot(xcsc(x)) ?

The derivative of-6cot(xcsc(x)) is -6(csc(x)-2csc^3(x))

What is the first derivative of-6cot(xcsc(x)) ?

The first derivative of-6cot(xcsc(x)) is -6(csc(x)-2csc^3(x))

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\frac{d}{d x} (- 6 cot (x) csc (x))

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

Solution steps

\frac{d}{d x} (- 6 cot (x) csc (x))

Take the constant out:

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

= - 6 \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)

= - 6 (\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)

= - 6 ((- csc^{2} (x)) csc (x) + (- cot (x) csc (x)) cot (x))

Simplify

- 6 ((- csc^{2} (x)) csc (x) + (- cot (x) csc (x)) cot (x)) : - 6 (csc (x) - 2 csc^{3} (x))

= - 6 (csc (x) - 2 csc^{3} (x))

\frac{\partial}{\partial x} ((1 + 2 x^{2}) (x - x^{2}))

(7.2) (2.8)

\int_{- 6}^{6} 58

x \to 4 lim (\frac{∣ x ∣}{x})

\frac{d}{d x} (\frac{1}{2 + x ^{2}})

What is the derivative of-6cot(xcsc(x)) ?
The derivative of-6cot(xcsc(x)) is -6(csc(x)-2csc^3(x))
What is the first derivative of-6cot(xcsc(x)) ?
The first derivative of-6cot(xcsc(x)) is -6(csc(x)-2csc^3(x))