What is the derivative of (7cos(x-8)/(sin(x))) ?

The derivative of (7cos(x-8)/(sin(x))) is (-7sin^2(x)-cos(x)(7cos(x)-8))/(sin^2(x))

What is the first derivative of (7cos(x-8)/(sin(x))) ?

The first derivative of (7cos(x-8)/(sin(x))) is (-7sin^2(x)-cos(x)(7cos(x)-8))/(sin^2(x))

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\frac{d}{d x} (\frac{7 cos ( x ) - 8}{sin ( x )})

\frac{- 7 sin ^{2} ( x ) - cos ( x ) ( 7 cos ( x ) - 8 )}{sin ^{2} ( x )}

Solution steps

\frac{d}{d x} (\frac{7 cos ( x ) - 8}{sin ( x )})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 7 cos ( x ) - 8 ) sin ( x ) - \frac{d}{d x} ( sin ( x ) ) ( 7 cos ( x ) - 8 )}{( sin ( x ) ) ^{2}}

\frac{d}{d x} (7 cos (x) - 8) = - 7 sin (x)

\frac{d}{d x} (sin (x)) = cos (x)

= \frac{( - 7 sin ( x ) ) sin ( x ) - cos ( x ) ( 7 cos ( x ) - 8 )}{( sin ( x ) ) ^{2}}

Simplify

\frac{( - 7 sin ( x ) ) sin ( x ) - cos ( x ) ( 7 cos ( x ) - 8 )}{sin ^{2} ( x )} : \frac{- 7 sin ^{2} ( x ) - cos ( x ) ( 7 cos ( x ) - 8 )}{sin ^{2} ( x )}

= \frac{- 7 sin ^{2} ( x ) - cos ( x ) ( 7 cos ( x ) - 8 )}{sin ^{2} ( x )}

\int 3 csc (x) cot (x) d x

\int \frac{x}{x ^{4} + 10} d x

\frac{x}{x - 1}

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

lo g_{10} ((arcsin (x))^{2})

What is the derivative of (7cos(x-8)/(sin(x))) ?
The derivative of (7cos(x-8)/(sin(x))) is (-7sin^2(x)-cos(x)(7cos(x)-8))/(sin^2(x))
What is the first derivative of (7cos(x-8)/(sin(x))) ?
The first derivative of (7cos(x-8)/(sin(x))) is (-7sin^2(x)-cos(x)(7cos(x)-8))/(sin^2(x))