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

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

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

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

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

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

Solution steps

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

Simplify

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

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

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

\frac{d}{d 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)

x \to 3 - lim (\frac{∣ 3 - x ∣}{x - 3})

\frac{\partial}{\partial x} (2 x^{2} - 6 y^{3} + 3 z^{2})

\int sin^{4} (x) cos^{5} (x) d x

\frac{d}{d x} (3 x - sin (x))

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