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)

n = 1 \sum \infty (3 n) x^{n}

\frac{\partial}{\partial x} (9 x y^{2})

\int_{0}^{2} (1 - 2 x) d x

\int \frac{2 x ^{3} + x ^{2} + 8 x - 12}{x ^{3} + 4 x} d x

(0) (1.2)

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)