why do we use dy/dx as ratio though it is not while solving the problems of integration by substitution
3360
Is $\frac{\textrm{d}y}{\textrm{d}x}$ not a ratio?
93539
Why is $M\frac{dv}{dt} = v_{rel} .\frac{dm}{dt}$ correct and $(M - dm)\frac{dv}{dt} = v_{rel} .\frac{dm}{dt}$ wrong?
125506
Why can I get two different results when calculating $\int \ln(z) \,dz$?
23975
What is the practical difference between a differential and a derivative?
86407
Why is it differential equations exist on an interval instead of a domain?
29296
Are there any special rules when making a substitution in an integral?
8502
Why aren't integration and differentiation inverses of each other?
119695
Understanding the relationship between differentiation and integration
114672
Why do we use the Lagrangian and Hamiltonian instead of other related functions?
91526
How do I convince my students that the choice of variable of integration is irrelevant?
126261
Extraneous solution from substituting in equations
68310
Why can partial derivatives be exchanged?
48050
Notation problem in integration: write $dx$ or ${\mathrm{d}}x$?
9211
$\int\frac{dx}{x-3y}$ when $y(x-y)^2=x$?
32642
The formalism behind integration by substitution
8711
Problems in the relation $a=v\frac{\mathrm{d}v}{\mathrm{d}x}$
128355
Does $e^{tx} + x = t - 1$ yield a solution/s to $\frac{dx}{dt} = \frac{e^{-tx} - x}{e^{-tx} + t}$?