Pochodne

Question 1

$(C)^\prime$

Accepted Answer

0

Question 2

$(x^n )^\prime$

Accepted Answer

$nx^{n-1}$

Question 3

${x}^\prime$

Accepted Answer

$1$

Question 4

$\left(\frac{a}{x}\right)^\prime$

Accepted Answer

$-\frac{a}{x^2}$

Question 5

$\left(\sqrt x\right)^\prime$

Accepted Answer

$\frac{1}{2\sqrt x}$

Question 6

$\left(a^x\right)^\prime$

Accepted Answer

$a^x\ln{a}$

Question 7

$\left(e^x\right)^\prime$

Accepted Answer

$e^x$

Question 8

$\left(\log_a{x}\right)^\prime$

Accepted Answer

$\frac{1}{x\ln{a}\ }$

Question 9

$\left(\ln{x}\right)^\prime$

Accepted Answer

$\frac{1}{x}$

Question 10

$\left(\sin{x}\right)^\prime$

Accepted Answer

$\cos{x}$

Question 11

$\left(\cos{x}\right)^\prime$

Accepted Answer

$-\sin{x}$

Question 12

$\left(tgx\right)^\prime$

Accepted Answer

$\frac{1}{\cos^2{x}}$

Question 13

$\left(ctgx\right)^\prime$

Accepted Answer

$-\frac{1}{\sin^2{x}}$

Question 14

$\left(\arcsin{x}\right)^\prime$

Accepted Answer

$\frac{1}{\sqrt{1-x^2}}$

Question 15

$\left(\arccos{x}\right)^\prime$

Accepted Answer

$-\frac{1}{\sqrt{1-x^2}}$

Question 16

$\left(arctgx\right)^\prime$

Accepted Answer

$\frac{1}{x^2+1}$

Question 17

$\left(arcctgx\right)^\prime$

Accepted Answer

$-\frac{1}{x^2+1}$

Question 18

$[a·f(x)]'$

Accepted Answer

$a·f'(x)$

Question 19

$[f(x)·g(x)]'$

Accepted Answer

$f'(x)g(x)+f(x)g'(x)$

Question 20

$\left[\frac{f\left(x\right)}{g\left(x\right)}\right]^\prime$

Accepted Answer

$\frac{f^\prime\left(x\right)g\left(x\right)-f\left(x\right)g^\prime\left(x\right)}{\left[g\left(x\right)\right]^2}$

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