3k views

### What is wrong with treating $\dfrac {dy}{dx}$ as a fraction? [duplicate]

If you think about the limit definition of the derivative, $dy$ represents $$\lim_{h\rightarrow 0}\dfrac {f(x+h)-f(x)}{h}$$, and $dx$ represents $$\lim_{h\rightarrow 0}$$ . So you have a ...
254 views

### How is an infinitesimal $dx$ different from $\Delta x\,$? [duplicate]

When I learned calc, I was always taught $$\frac{df}{dx}= f'(x) = \lim_{h\rightarrow 0} \frac{f(x+h)-f(x)}{(x+h)-x}$$ But I have heard $dx$ is called an infinitesimal and I don't know what this ...
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### $dx=\frac {dx}{dt}dt$. Why is this equality true and what does it mean? [duplicate]

$dx=\frac {dx}{dt}dt$. I know that this deduction is obvious from the chain rule, given that we treat our dx and dt as just numbers. But I find it quite unsatisfactory to think of it in that sense. ...
81 views

### Differential Notation Magic in Integration by u-Substitution [duplicate]

I'm really confused now. I always thought that the differential notation $\frac{df}{dx}$ was just that, a notation. But somehow when doing integration by u-substitution I'm told that you can turn ...
136 views

### Why do we treat differential notation as a fraction in u-substitution method [duplicate]

How did we come to know that treating the differential notation as a fraction will help us in finding the integral. And how do we know about its validity? How can $\frac{dy}{dx}$ be treated as a ...
150 views

### $dy\over dx$ is one things but why in integration we can treat it as 2 different terms [duplicate]

when i am learning differentiation, my lectuer tell us that the deriative $dy\over dx$ is one things, it is not the ration between dy and dx. However when i learn about integrating, sometime we need ...
83 views