How do we go from $f'(x) = \frac{dy}{dx}$ to $dy = f'(x)dx$?
3360
Is $\frac{\textrm{d}y}{\textrm{d}x}$ not a ratio?
66181
Find the derivative of the function
51291
How can I express $\int \frac{1}{f'(x)}$ in terms of $f(x)$
4735
Proof for alternative definition of the derivative
21879
Show that if $\lim_{x\to a}f'(x) = A$ then $f'(a)$ exists and equals A
99795
Derivative of piece-wise function given by $x\sin\frac1x$ at $x=0$
38894
Solve $x=y\frac{dy}{dx}-\left(\frac{dy}{dx}\right)^{2}$
146888
Derivative of function with 2 variables
885
Why is the 2nd derivative written as $\frac{\mathrm d^2y}{\mathrm dx^2}$?
41720
Getting equation from differential equations
69008
$f'(x) = [f(x)]^{2}$. Prove $f(x) = 0 $
56275
Vector derivative w.r.t its transpose $\frac{d(Ax)}{d(x^T)}$
144644
Solution of $\frac{dy}{dx}=\frac{1}{xy(x^2 \sin y^2+1)}$
145496
Show $\lim_{h \to \ 0} \frac{f(x + 2h) - 2f(x+h) + f(x)}{h^{2}} = f''(x)$ Proof verification
134871
Using definition of derivative to differentiate $f(x)= \sqrt{x}+1$
66406
How to calculate $f(x)$ in $f(f(x)) = e^x$?
62055
Solve $\frac{d}{dx}f(x)=f(x-1)$