What is the derivative of y=(3+csc(x))/(7-csc(x)) ?

The derivative of y=(3+csc(x))/(7-csc(x)) is -(10cot(x)csc(x))/((7-csc(x))^2)

What is the first derivative of y=(3+csc(x))/(7-csc(x)) ?

The first derivative of y=(3+csc(x))/(7-csc(x)) is -(10cot(x)csc(x))/((7-csc(x))^2)

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derivative of

y = \frac{3 + csc ( x )}{7 - csc ( x )}

- \frac{10 cot ( x ) csc ( x )}{( 7 - csc ( x ) ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{3 + 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} ( 3 + csc ( x ) ) ( 7 - csc ( x ) ) - \frac{d}{d x} ( 7 - csc ( x ) ) ( 3 + csc ( x ) )}{( 7 - csc ( x ) ) ^{2}}

\frac{d}{d x} (3 + 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 ) ( 3 + csc ( x ) )}{( 7 - csc ( x ) ) ^{2}}

Simplify

\frac{( - cot ( x ) csc ( x ) ) ( 7 - csc ( x ) ) - cot ( x ) csc ( x ) ( 3 + csc ( x ) )}{( 7 - csc ( x ) ) ^{2}} : - \frac{10 cot ( x ) csc ( x )}{( 7 - csc ( x ) ) ^{2}}

= - \frac{10 cot ( x ) csc ( x )}{( 7 - csc ( x ) ) ^{2}}

\frac{2 x}{( x ^{2} - 5 ) ^{3}}, at x = 0

\int \frac{1}{x ^{3} x ^{2} - 81} d x

\frac{d}{d x} ((3 x - 1) (x - 2)^{4})

\frac{d y}{d x} (1 + x) - x y = x + x^{2}

What is the derivative of y=(3+csc(x))/(7-csc(x)) ?
The derivative of y=(3+csc(x))/(7-csc(x)) is -(10cot(x)csc(x))/((7-csc(x))^2)
What is the first derivative of y=(3+csc(x))/(7-csc(x)) ?
The first derivative of y=(3+csc(x))/(7-csc(x)) is -(10cot(x)csc(x))/((7-csc(x))^2)