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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?

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    You aren't mixing it, because you are not using primes and Leibnitz notation on the same side of the equal sign; even so, it's still okay to mix the two with some care. E.g.,$\frac{d^2f}{dx^2} = \frac{d}{dx}f'(x)$is understandable enough to be acceptable.2011-04-14

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Yes, it is acceptable to mix notations.

(Answered by Arturo Magidin & Jack)