What is (\partial)/(\partial x)((x^2)/(sin^2(x))) ?

The answer to (\partial)/(\partial x)((x^2)/(sin^2(x))) is 2xcsc^2(x)-2x^2csc^2(x)cot(x)

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(\partial)/(\partial x)((x^2)/(sin^2(x)))

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

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

Solution steps

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

Simplify

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

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

\frac{\partial}{\partial z} (\frac{( x + y )}{y + z})

x \to 2 + lim (- \frac{5}{x - 2})

\int_{4}^{- 4} (- 7) d x

t^{2} + e^{- t} sin (2 t)

\int - e^{- 3 x} d x

What is (\partial)/(\partial x)((x^2)/(sin^2(x))) ?
The answer to (\partial)/(\partial x)((x^2)/(sin^2(x))) is 2xcsc^2(x)-2x^2csc^2(x)cot(x)