What is the d/(dq)((1+csc(q))cos(q)) ?

The d/(dq)((1+csc(q))cos(q)) is -sin(q)-csc^2(q)

What is the first d/(dq)((1+csc(q))cos(q)) ?

The first d/(dq)((1+csc(q))cos(q)) is -sin(q)-csc^2(q)

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\frac{d}{d q} ((1 + csc (q)) cos (q))

- sin (q) - csc^{2} (q)

Solution steps

\frac{d}{d q} ((1 + csc (q)) cos (q))

Simplify

(1 + csc (q)) cos (q) : cos (q) + cot (q)

= \frac{d}{d q} (cos (q) + cot (q))

Apply the Sum/Difference Rule:

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

= \frac{d}{d q} (cos (q)) + \frac{d}{d q} (cot (q))

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

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

= - sin (q) - csc^{2} (q)

What is the d/(dq)((1+csc(q))cos(q)) ?
The d/(dq)((1+csc(q))cos(q)) is -sin(q)-csc^2(q)
What is the first d/(dq)((1+csc(q))cos(q)) ?
The first d/(dq)((1+csc(q))cos(q)) is -sin(q)-csc^2(q)