What is the derivative of (4+csc(x)/(8-csc(x))) ?

The derivative of (4+csc(x)/(8-csc(x))) is -(12cot(x)csc(x))/((8-csc(x))^2)

What is the first derivative of (4+csc(x)/(8-csc(x))) ?

The first derivative of (4+csc(x)/(8-csc(x))) is -(12cot(x)csc(x))/((8-csc(x))^2)

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\frac{d}{d x} (\frac{4 + csc ( x )}{8 - csc ( x )})

- \frac{12 cot ( x ) csc ( x )}{( 8 - csc ( x ) ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{4 + csc ( x )}{8 - csc ( x )})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 4 + csc ( x ) ) ( 8 - csc ( x ) ) - \frac{d}{d x} ( 8 - csc ( x ) ) ( 4 + csc ( x ) )}{( 8 - csc ( x ) ) ^{2}}

\frac{d}{d x} (4 + csc (x)) = - cot (x) csc (x)

\frac{d}{d x} (8 - csc (x)) = cot (x) csc (x)

= \frac{( - cot ( x ) csc ( x ) ) ( 8 - csc ( x ) ) - cot ( x ) csc ( x ) ( 4 + csc ( x ) )}{( 8 - csc ( x ) ) ^{2}}

Simplify

\frac{( - cot ( x ) csc ( x ) ) ( 8 - csc ( x ) ) - cot ( x ) csc ( x ) ( 4 + csc ( x ) )}{( 8 - csc ( x ) ) ^{2}} : - \frac{12 cot ( x ) csc ( x )}{( 8 - csc ( x ) ) ^{2}}

= - \frac{12 cot ( x ) csc ( x )}{( 8 - csc ( x ) ) ^{2}}

\int 4 x^{3} ln (x) d x

\frac{d}{d x} (c x + ln (cos (x)))

y^{^{'}} + r y^{^{''}} = 0

\frac{d}{d x} ((x^{2} + 2)^{- 5} (cos (x)))

\int_{1200}^{1210} 0.1 x^{2} d x

What is the derivative of (4+csc(x)/(8-csc(x))) ?
The derivative of (4+csc(x)/(8-csc(x))) is -(12cot(x)csc(x))/((8-csc(x))^2)
What is the first derivative of (4+csc(x)/(8-csc(x))) ?
The first derivative of (4+csc(x)/(8-csc(x))) is -(12cot(x)csc(x))/((8-csc(x))^2)