What is the derivative of-csc(x-cos(x)) ?

The derivative of-csc(x-cos(x)) is cot(x)csc(x)+sin(x)

What is the first derivative of-csc(x-cos(x)) ?

The first derivative of-csc(x-cos(x)) is cot(x)csc(x)+sin(x)

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\frac{d}{d x} (- csc (x) - cos (x))

cot (x) csc (x) + sin (x)

Solution steps

\frac{d}{d x} (- csc (x) - cos (x))

Apply the Sum/Difference Rule:

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

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

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

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

= - (- cot (x) csc (x)) - (- sin (x))

Simplify

= cot (x) csc (x) + sin (x)

What is the derivative of-csc(x-cos(x)) ?
The derivative of-csc(x-cos(x)) is cot(x)csc(x)+sin(x)
What is the first derivative of-csc(x-cos(x)) ?
The first derivative of-csc(x-cos(x)) is cot(x)csc(x)+sin(x)