Question on notation of differentials Is the following notation acceptable, specifically last part of the last line?
$$f(x) = \csc^4(x) = (\csc(x))^4$$
Let 
$$u =\csc(x) \rightarrow f(x) = u^4$$
$$f'(x) = \frac{du}{dx} \times \frac{df(x)}{du}$$
$$...$$

Edit: Reworded question: Is it OK to mix Leibniz's and Lagrange's notation?

Yes, it is acceptable to mix notations.
(Answered by Arturo Magidin & Jack)
