f	f^′
c	0
x	1
x^n	nx^n − 1
$$\frac{a}{x}$$	$$- \frac{a}{x^{2}}$$
sinx	cosx
cosx	−sinx
tgx	$$\frac{1}{\cos^{2}x}$$
ctgx	$$- \frac{1}{\sin^{2}x}$$
a^x	a^xlna
x^x	x^x(1 + lnx)
lnx	$$\frac{1}{x}$$
logax	$$\frac{1}{\text{xlna}}$$
arcsinx	$$\frac{1}{\sqrt{1 - x^{2}}}$$
arccosx	$$- \frac{1}{\sqrt{1 - x^{2}}}$$
arctgx	$$\frac{1}{1 + x^{2}}$$
arcctgx	$$- \frac{1}{1 + x^{2}}$$
$$\sqrt{x}$$	$$\frac{1}{2\sqrt{x}}$$
$$\sqrt[n]{x}$$	$$\frac{1}{n\sqrt[n]{x^{n - 1}}}$$

∫f	f
∫0 dx	C
∫x^n dx	$\frac{x^{n + 1}}{n + 1}$ +C
$$\int_{}^{}\frac{1}{x}\ \text{dx}$$	ln|x| + C
∫a^x dx	$$\frac{a^{x}}{\text{lna}} + \ C$$
∫sinx dx	−cosx + C
∫cosx dx	sinx + C
$$\int_{}^{}\frac{\text{dx}}{\sin^{2}x}$$	−ctgx + C
$$\int_{}^{}\frac{\text{dx}}{\cos^{2}x}$$	tgx + C
$$\int_{}^{}\frac{\text{dx}}{1 + \ x^{2}}$$	arctgx + C
$$\int_{}^{}\frac{\text{dx}}{\sqrt{1 - x^{2}}}$$	arcsinx + C