What is the derivative of y= 8/(sin(x))+1/(cot(x)) ?

The derivative of y= 8/(sin(x))+1/(cot(x)) is (-8cot(x)+sec(x)tan(x))/(sin(x))

What is the first derivative of y= 8/(sin(x))+1/(cot(x)) ?

The first derivative of y= 8/(sin(x))+1/(cot(x)) is (-8cot(x)+sec(x)tan(x))/(sin(x))

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derivative of

y = \frac{8}{sin ( x )} + \frac{1}{cot ( x )}

\frac{- 8 cot ( x ) + sec ( x ) tan ( x )}{sin ( x )}

Solution steps

\frac{d}{d x} (\frac{8}{sin ( x )} + \frac{1}{cot ( x )})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (\frac{8}{sin ( x )}) + \frac{d}{d x} (\frac{1}{cot ( x )})

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

\frac{d}{d x} (\frac{1}{cot ( x )}) = sec^{2} (x)

= - \frac{8 cot ( x )}{sin ( x )} + sec^{2} (x)

Simplify

- \frac{8 cot ( x )}{sin ( x )} + sec^{2} (x) : \frac{- 8 cot ( x ) + sec ( x ) tan ( x )}{sin ( x )}

= \frac{- 8 cot ( x ) + sec ( x ) tan ( x )}{sin ( x )}

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f (x) = \frac{6}{( 1 + e ^{- x} ) , at ( 0 , 3 )}

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What is the derivative of y= 8/(sin(x))+1/(cot(x)) ?
The derivative of y= 8/(sin(x))+1/(cot(x)) is (-8cot(x)+sec(x)tan(x))/(sin(x))
What is the first derivative of y= 8/(sin(x))+1/(cot(x)) ?
The first derivative of y= 8/(sin(x))+1/(cot(x)) is (-8cot(x)+sec(x)tan(x))/(sin(x))