What is the derivative of 3csc(x+5/x) ?

The derivative of 3csc(x+5/x) is -3cot(x)csc(x)-5/(x^2)

What is the first derivative of 3csc(x+5/x) ?

The first derivative of 3csc(x+5/x) is -3cot(x)csc(x)-5/(x^2)

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

- 3 cot (x) csc (x) - \frac{5}{x ^{2}}

Solution steps

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

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (3 csc (x)) + \frac{d}{d x} (\frac{5}{x})

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

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

= - 3 cot (x) csc (x) - \frac{5}{x ^{2}}

What is the derivative of 3csc(x+5/x) ?
The derivative of 3csc(x+5/x) is -3cot(x)csc(x)-5/(x^2)
What is the first derivative of 3csc(x+5/x) ?
The first derivative of 3csc(x+5/x) is -3cot(x)csc(x)-5/(x^2)