Question

найти произвольную
пожалуй помогите !!
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Answer 1

$y = 2x - 3$

$y' = (2x - 3)' = 2$

$y = \frac{1}{x^2}$

$y' = (\frac{1}{x^2})' = (x^{-2})' = -2\cdot x^{-2-1} = -\frac{2}{x^3}$

$y = 5^x$

$y' = (5^x)' = (e^{x\cdot\ln(5)})' = e^{x\cdot\ln(5)}\cdot(x\cdot\ln(5))' =$

$= 5^x\cdot\ln(5)$

$y = x^{\frac{2}{5}}\cdot\log_3 (x)$

$y' = (x^{\frac{2}{5}})'\cdot\log_3(x) + x^{\frac{2}{5}}\cdot(\log_3(x))' =$

$= \frac{2}{5}\cdot x^{-\frac{3}{5}}\cdot\log_3(x) + x^{\frac{2}{5}}\cdot\frac{1}{x\cdot\ln(3)}$

$y = x^{10}$

$y' = 10\cdot x^9$

$y = \sqrt[5]{x^3} = x^{\frac{3}{5}}$

$y' = \frac{3}{5}\cdot x^{-\frac{2}{5}}$

$y = log_{10} x$

$y' = (\frac{\ln(x)}{\ln(10)})' = \frac{1}{x\cdot\ln(10)}$