What is the derivative of (csc^3(x)/(ln(x^2))) ?

The derivative of (csc^3(x)/(ln(x^2))) is -(csc^3(x)(3xcot(x)ln(x)+1))/(2xln^2(x))

What is the first derivative of (csc^3(x)/(ln(x^2))) ?

The first derivative of (csc^3(x)/(ln(x^2))) is -(csc^3(x)(3xcot(x)ln(x)+1))/(2xln^2(x))

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

- \frac{csc ^{3} ( x ) ( 3 x cot ( x ) ln ( x ) + 1 )}{2 x ln ^{2} ( x )}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

= - \frac{csc ^{3} ( x ) ( 3 x cot ( x ) ln ( x ) + 1 )}{2 x ln ^{2} ( x )}

\frac{\partial}{\partial x} (y^{2} sin (4 x))

\frac{d}{d x} (2 ln (4 x))

\frac{d}{d x} (r x + s)

\int (2 x + 3)^{- 1} d x

\frac{d}{d s} (\frac{s - s}{s ^{2}})

What is the derivative of (csc^3(x)/(ln(x^2))) ?
The derivative of (csc^3(x)/(ln(x^2))) is -(csc^3(x)(3xcot(x)ln(x)+1))/(2xln^2(x))
What is the first derivative of (csc^3(x)/(ln(x^2))) ?
The first derivative of (csc^3(x)/(ln(x^2))) is -(csc^3(x)(3xcot(x)ln(x)+1))/(2xln^2(x))