Question

Differentiate R(w) = csc(7w) using the Chain Rule.
Can somebody answer and explain this for me? I'm really lost.

Answer 1

The derivative of csc u is - csc u cot u du

In your problem, let u = 7w.

So its derivative is - csc (7w) cot (7w) times 7

Final answer: -7 csc(7w) cot (7w).

Answer 2

csc(7w) = \( \frac{1}{\sin(7w)}\)

you can make that to the -1 power:
\[ \left( \sin(7w)\right)^{-1} \]
now use the exponent rule: \( d x^n= n x^{n-1} dx \)