What is the derivative of (csc(3x)/(x^3)) ?

The derivative of (csc(3x)/(x^3)) is -(3csc(3x)(xcot(3x)+1))/(x^4)

What is the first derivative of (csc(3x)/(x^3)) ?

The first derivative of (csc(3x)/(x^3)) is -(3csc(3x)(xcot(3x)+1))/(x^4)

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\frac{d}{d x} (\frac{csc ( 3 x )}{x ^{3}})

- \frac{3 csc ( 3 x ) ( x cot ( 3 x ) + 1 )}{x ^{4}}

Solution steps

\frac{d}{d x} (\frac{csc ( 3 x )}{x ^{3}})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( csc ( 3 x ) ) x ^{3} - \frac{d}{d x} ( x ^{3} ) csc ( 3 x )}{( x ^{3} ) ^{2}}

\frac{d}{d x} (csc (3 x)) = - cot (3 x) csc (3 x) \cdot 3

\frac{d}{d x} (x^{3}) = 3 x^{2}

= \frac{( - cot ( 3 x ) csc ( 3 x ) \cdot 3 ) x ^{3} - 3 x ^{2} csc ( 3 x )}{( x ^{3} ) ^{2}}

Simplify

\frac{( - cot ( 3 x ) csc ( 3 x ) \cdot 3 ) x ^{3} - 3 x ^{2} csc ( 3 x )}{( x ^{3} ) ^{2}} : - \frac{3 csc ( 3 x ) ( x cot ( 3 x ) + 1 )}{x ^{4}}

= - \frac{3 csc ( 3 x ) ( x cot ( 3 x ) + 1 )}{x ^{4}}

\int \frac{x - 4}{x ^{9}} d x

\frac{d}{d x} (x^{\frac{5}{3}})

2 t e^{- 5 t}

\frac{d}{d x} (10 x - 1.86 x^{2})

\frac{\partial}{\partial x} (y^{8 x})

What is the derivative of (csc(3x)/(x^3)) ?
The derivative of (csc(3x)/(x^3)) is -(3csc(3x)(xcot(3x)+1))/(x^4)
What is the first derivative of (csc(3x)/(x^3)) ?
The first derivative of (csc(3x)/(x^3)) is -(3csc(3x)(xcot(3x)+1))/(x^4)