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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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It shouldn't be $$\frac{df(x)}{du},$$ but rather $$\frac{df(u)}{du}.$$ This is the Chain Rule, so$$f'(x) = f'(u)u'(x) = \frac{d}{du}f(u)\times\frac{d}{dx}u(x).$$ –  Arturo Magidin Apr 14 '11 at 20:41
    
I think the question can be made to be more precise. The function $csc(x)$ here is not the essential part of your question. This may be helpful to clarify your "notation" question. –  Jack Apr 14 '11 at 20:47
    
@Jack True, good point. My question perhaps should have been "is $\frac{df(u)}{du}$ correct notation? I was nervous to mix Leibniz's and Lagrange's notation. But I gather from Arturo's response that this is acceptable? –  Danny King Apr 14 '11 at 20:56
    
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. –  Arturo Magidin Apr 14 '11 at 21:47
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1 Answer 1

up vote 1 down vote accepted

Yes, it is acceptable to mix notations.

(Answered by Arturo Magidin & Jack)

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