Logically, why is $\frac{d}{dx}(\ln{x}) = \frac{d}{dx}(\ln{ax})$?
95068
Integral of $\frac{1}{2x}$
73099
Why is $d(x^2)= 2xdx$?
68854
Proving $\mathcal{F}\left(\frac{d^n}{dx^n} f(x)\right)=(ik)^n\mathcal{F}(f(x))$.
105707
A proof of $\int_{0}^{1}\left( \frac{\ln t}{1-t}\right)^2\,\mathrm{d}t=\frac{\pi^2}{3}$
63251
Evaluation of $\int^1_0\frac{x^b-x^a}{\ln x} d x=\ln{{\frac{1+b}{1+a}}}$
128764
How does $y[x] = a x^r$ when $y'[x] = \frac{(r y[x])}{x}$ and $y[1] = a$
137614
$\left|\frac{x}{|x|}-\frac{y}{|y|}\right|\leq |x-y|$, for $|x|, |y|\geq 1$?
67622
Proving of Integral $\int_{0}^{\infty}\frac{e^{-bx}-e^{-ax}}{x}dx = \ln\left(\frac{a}{b}\right)$
46310
Showing that $ \int_{0}^{1} \frac{x-1}{\ln(x)} \mathrm dx=\ln2 $
109192
Intuitive reason why $ \frac1j > \int_{j}^{j+1} \frac1x dx $ for $j$ < $x$
49408
Proof of the derivative of ln(x)
152895
What is wrong with this derivation of $\frac{d}{dx}x^2$?
56275
Vector derivative w.r.t its transpose $\frac{d(Ax)}{d(x^T)}$
91059
Why is $\frac{d^n}{dx^n}(y(x))$ the notation for the $n$th derivative of $y(x)$, instead of $\frac{d^n}{d^nx}(y(x))$?
95265
Why is it legitimate to solve the differential equation $\frac{dy}{dx}=\frac{y}{x}$ by taking $\int \frac{1}{y}\ dy=\int \frac{1}{x}\ dx$?
128953
Why $\frac{\log(x)}{\log(y)}$ gives the same value as $\frac{\ln(x)}{\ln(y)}$
99753
How to prove $\int_0^1\frac{1-x}{(\ln x)(1+x)}\ dx=\ln\left(\frac2{\pi}\right)$?