Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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?

share|cite|improve this question
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
up vote 1 down vote accepted

Yes, it is acceptable to mix notations.

(Answered by Arturo Magidin & Jack)

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.