What is the derivative of csc(x+cot(x)) ?

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

What is the first derivative of csc(x+cot(x)) ?

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

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\frac{d}{d x} (csc (x) + cot (x))

- cot (x) csc (x) - csc^{2} (x)

Solution steps

\frac{d}{d x} (csc (x) + cot (x))

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (csc (x)) + \frac{d}{d x} (cot (x))

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

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

= - cot (x) csc (x) - csc^{2} (x)

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