# 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?

-
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