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dy/dx represents the derivative of y wrt x. We are taught that it is not the ratio of dy and dx but a limiting form that the ratio of the change of the dependent variable wrt the change of the independent variable takes when the latter tends to zero. Now if dy/dx is just a symbol representing the derivative how can we separate dy n dx during the process of integration i.e if dy/dx=f(x) then we can write dy=f(x)dx. Are dy n dx real numbers or what do they represent . What exactly are differential. Plz explain elaborately

Shiksharthi Sharma
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  • See also http://math.stackexchange.com/questions/143222/what-does-dx-mean, http://math.stackexchange.com/questions/200393/what-is-dx-in-integration, http://math.stackexchange.com/questions/27425/what-am-i-doing-when-i-separate-the-variables-of-a-differential-equation, and many other questions on this site. – Hans Lundmark Nov 20 '16 at 18:46

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As I know $df$ in which $f$ is a differentable function in $x$ ($f'(x)<\infty$), is defined as $$f'(x)\Delta(x)$$. It is not far seeing that $\Delta(x)=dx$. When we work with $df/dx$ indeed we work with ratio $$\Delta(f)/\Delta(x)=[f(x+\Delta(x))-f(x)]/\Delta(x)$$ which is eqaul to $f'(x)+\epsilon(\Delta(x))$. This last term is a function in which gets 0 when $\Delta(x)\to 0$. I hope as a non native one, could explain a bit clear wthe difference between them.

Mikasa
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