What is the derivative of sin(x+8/3 cot(x)) ?

The derivative of sin(x+8/3 cot(x)) is cos(x)-8/3 csc^2(x)

What is the first derivative of sin(x+8/3 cot(x)) ?

The first derivative of sin(x+8/3 cot(x)) is cos(x)-8/3 csc^2(x)

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\frac{d}{d x} (sin (x) + \frac{8}{3} cot (x))

cos (x) - \frac{8}{3} csc^{2} (x)

Solution steps

\frac{d}{d x} (sin (x) + \frac{8}{3} cot (x))

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (sin (x)) + \frac{d}{d x} (\frac{8}{3} cot (x))

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

\frac{d}{d x} (\frac{8}{3} cot (x)) = - \frac{8}{3} csc^{2} (x)

= cos (x) - \frac{8}{3} csc^{2} (x)

\frac{d}{d x} (\frac{1}{2} x + 1)

\frac{d}{d x} (\frac{9 x}{( x ^{2} + 1 ) ^{\frac{3}{5}}})

\frac{d}{d x} (\frac{x ^{5} - 5 x}{5})

\int \frac{x}{a + b x ^{2}} d x

\frac{d}{d x} (x^{3} + x^{5})

What is the derivative of sin(x+8/3 cot(x)) ?
The derivative of sin(x+8/3 cot(x)) is cos(x)-8/3 csc^2(x)
What is the first derivative of sin(x+8/3 cot(x)) ?
The first derivative of sin(x+8/3 cot(x)) is cos(x)-8/3 csc^2(x)