query: If $F=m\dfrac{dv}{dt}$ why is it incorrect to write $F\,dt=m\,dv$?
positive_passages.docid: 3360
positive_passages.text: Is $\frac{\textrm{d}y}{\textrm{d}x}$ not a ratio?
negative_passages.docid: 43430
negative_passages.text: What exactly does $\frac{dx}{dy}$ mean?
negative_passages.docid: 43385
negative_passages.text: Why is $\frac{\operatorname dy'}{\operatorname dy}$ zero, since $y'$ depends on $y$?
negative_passages.docid: 113343
negative_passages.text: $f$ is constant if derivative equals zero
negative_passages.docid: 973
negative_passages.text: Is the property "being a derivative" preserved under multiplication and composition?
negative_passages.docid: 77074
negative_passages.text: If $ f(f(f(x)))=x$, does$ f(x)=x$ necessarily follow?
negative_passages.docid: 34790
negative_passages.text: Find $f(1)$ from equation $\int_{0}^{x}f(t)dt = x+\int_{x}^{1}tf(t)dt$
negative_passages.docid: 86367
negative_passages.text: Computing $f(x)$ if $\int_1^{xy} f(t) dt = y \int_1^x f(t) dt + x\int_1^y f(t) dt$ and $f(1) = 3$
negative_passages.docid: 53610
negative_passages.text: What is the difference between $Q=\Delta U+W$ and $\Delta U=Q+W$?
negative_passages.docid: 55680
negative_passages.text: The relationship of ${\frak m+m=m}$ to AC
negative_passages.docid: 16644
negative_passages.text: Why does cancellation of dots $\frac{\partial \dot{\mathbf{r}}_i}{\partial \dot{q}_j} = \frac{\partial \mathbf{r}_i}{\partial q_j}$ work?
negative_passages.docid: 95429
negative_passages.text: If $f$ is continuous with $ \int_0^{\infty}f(t)\,dt<\infty$ then which are correct?
negative_passages.docid: 91059
negative_passages.text: Why is $\frac{d^n}{dx^n}(y(x))$ the notation for the $n$th derivative of $y(x)$, instead of $\frac{d^n}{d^nx}(y(x))$?
negative_passages.docid: 56032
negative_passages.text: How come $\frac{1}{1-x}$ and $\frac{x}{1-x}$ have the same derivative?
negative_passages.docid: 29389
negative_passages.text: Why does $k/m=\omega^2$ for harmonic motion?
negative_passages.docid: 12092
negative_passages.text: When can one write $a=v \cdot dv/dx$?
negative_passages.docid: 31961
negative_passages.text: Given fields $M/E/F$, why does $[M:F] = [M:E][E:F]$?