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

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

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

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

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derivative of

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

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

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

\frac{d}{d x} (x^{2} cot (x) csc (x)) = 2 x cot (x) csc (x) + (csc (x) - 2 csc^{3} (x)) x^{2}

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

Simplify

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

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

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