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

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

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

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

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

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

Solution steps

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

Simplify

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

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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