Question

Тема "производные" 1. y=³√(x²+x+2) 2. y=(3x)/(2-x) если y(2) 3. y=x²×e^x^2 4. y=5^x+lnx+8 5. y=3ctgx+ctg³x если у`(π/3)

Answer 1

1.
$y'= \frac{1}3(x^2+x+2)^{- \frac{2}{3} }*(2x+1)= \frac{2x+1}{3* \sqrt[3]{(x^2+x+2)^2} }$

2.
$y'= \frac{3(2-x)+3x}{(2-x)^2} = \frac{6-3x+3x}{(2-x)^2}= \frac{6}{(2-x)^2}$

3.
$y'=2x*e^{x^2}+x^2*e^{x^2}*2x=2x*e^{x^2}(1+x^2)$

4.
$y'=5^{x}*lnx+ \frac{1}{x}$

5.
$y'=- \frac{3}{sin^2x}+3ctg^2x*(- \frac{1}{sin^2x} )=- \frac{3}{sin^2x}- \frac{3cos^2x}{sin^2x*sin^2x} = \\ \\ =-3( \frac{sin^2x+cos^2x}{sin^4x} )=- \frac{3}{sin^4x}$