What is the derivative of ((x^2)/(sin(x))) ?

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

What is the first derivative of ((x^2)/(sin(x))) ?

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

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

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

Solution steps

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

Simplify

\frac{( x ^{2} )}{sin ( x )} : x^{2} csc (x)

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

y^{^{'}} - e^{6 x + y} = 0

\int x (x + 1)^{4} d x

(arcsin (2 x))^{^{'}}

y = (arctan (3 x)) 2

y^{^{''}} - 9 y = e^{3 x}

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