What is the derivative of x^2csc(5x) ?

The derivative of x^2csc(5x) is 2xcsc(5x)-5x^2cot(5x)csc(5x)

What is the first derivative of x^2csc(5x) ?

The first derivative of x^2csc(5x) is 2xcsc(5x)-5x^2cot(5x)csc(5x)

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\frac{d}{d x} (x^{2} csc (5 x))

2 x csc (5 x) - 5 x^{2} cot (5 x) csc (5 x)

Solution steps

\frac{d}{d x} (x^{2} csc (5 x))

Apply the Product Rule:

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

f = x^{2}, g = csc (5 x)

= \frac{d}{d x} (x^{2}) csc (5 x) + \frac{d}{d x} (csc (5 x)) x^{2}

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

\frac{d}{d x} (csc (5 x)) = - cot (5 x) csc (5 x) \cdot 5

= 2 x csc (5 x) + (- cot (5 x) csc (5 x) \cdot 5) x^{2}

Simplify

= 2 x csc (5 x) - 5 x^{2} cot (5 x) csc (5 x)

What is the derivative of x^2csc(5x) ?
The derivative of x^2csc(5x) is 2xcsc(5x)-5x^2cot(5x)csc(5x)
What is the first derivative of x^2csc(5x) ?
The first derivative of x^2csc(5x) is 2xcsc(5x)-5x^2cot(5x)csc(5x)