What is the derivative of sin(x+5/6 cot(x)) ?

The derivative of sin(x+5/6 cot(x)) is cos(x)-5/6 csc^2(x)

What is the first derivative of sin(x+5/6 cot(x)) ?

The first derivative of sin(x+5/6 cot(x)) is cos(x)-5/6 csc^2(x)

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\frac{d}{d x} (sin (x) + \frac{5}{6} cot (x))

cos (x) - \frac{5}{6} csc^{2} (x)

Solution steps

\frac{d}{d x} (sin (x) + \frac{5}{6} cot (x))

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (sin (x)) + \frac{d}{d x} (\frac{5}{6} cot (x))

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

\frac{d}{d x} (\frac{5}{6} cot (x)) = - \frac{5}{6} csc^{2} (x)

= cos (x) - \frac{5}{6} csc^{2} (x)

What is the derivative of sin(x+5/6 cot(x)) ?
The derivative of sin(x+5/6 cot(x)) is cos(x)-5/6 csc^2(x)
What is the first derivative of sin(x+5/6 cot(x)) ?
The first derivative of sin(x+5/6 cot(x)) is cos(x)-5/6 csc^2(x)