What is the derivative of (8+csc(x)/(7-csc(x))) ?

The derivative of (8+csc(x)/(7-csc(x))) is -(15cot(x)csc(x))/((7-csc(x))^2)

What is the first derivative of (8+csc(x)/(7-csc(x))) ?

The first derivative of (8+csc(x)/(7-csc(x))) is -(15cot(x)csc(x))/((7-csc(x))^2)

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\frac{d}{d x} (\frac{8 + csc ( x )}{7 - csc ( x )})

- \frac{15 cot ( x ) csc ( x )}{( 7 - csc ( x ) ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{8 + csc ( x )}{7 - csc ( x )})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 8 + csc ( x ) ) ( 7 - csc ( x ) ) - \frac{d}{d x} ( 7 - csc ( x ) ) ( 8 + csc ( x ) )}{( 7 - csc ( x ) ) ^{2}}

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

\frac{d}{d x} (7 - csc (x)) = cot (x) csc (x)

= \frac{( - cot ( x ) csc ( x ) ) ( 7 - csc ( x ) ) - cot ( x ) csc ( x ) ( 8 + csc ( x ) )}{( 7 - csc ( x ) ) ^{2}}

Simplify

\frac{( - cot ( x ) csc ( x ) ) ( 7 - csc ( x ) ) - cot ( x ) csc ( x ) ( 8 + csc ( x ) )}{( 7 - csc ( x ) ) ^{2}} : - \frac{15 cot ( x ) csc ( x )}{( 7 - csc ( x ) ) ^{2}}

= - \frac{15 cot ( x ) csc ( x )}{( 7 - csc ( x ) ) ^{2}}

x \to \infty lim (\frac{3}{5 x})

\int 9 e^{3 x} d x

\int x e^{3 x} + e^{x} d x

f (x) = e^{2 x} (x^{3} + 1)

\frac{d ^{2}}{d x ^{2}} ((4 x^{2} + 9 x) cos (x))

What is the derivative of (8+csc(x)/(7-csc(x))) ?
The derivative of (8+csc(x)/(7-csc(x))) is -(15cot(x)csc(x))/((7-csc(x))^2)
What is the first derivative of (8+csc(x)/(7-csc(x))) ?
The first derivative of (8+csc(x)/(7-csc(x))) is -(15cot(x)csc(x))/((7-csc(x))^2)