Question

решите пожалйста производные 1)f(x)=(sin^2)x-(cos^2)x
2)y=(sin2x-cos2x)/(sin2x+cos2x)
3)sqrt(x)^5 arcsinx-(tg/x^2)
4)(1/sqrt(x^3)^4)+(3/x^2)-5x

Answer 1

$y= frac{sin2x-cos2x }{sin2x+cos2x}\\y'= frac{2cos2x+2sin2x}{2cos2x-2sin2x}= frac{cos2x+sin2x}{cos2x-sin2x}\\\y= sqrt{x^5} cdot arcsin(tgx^2)\\y'=frac{5}{2}x^{frac{3}{2}}cdot arcsin(tgx^2)+sqrt{x^5}cdot frac{1}{sqrt{1-tg^2(x^2)}}cdot frac{1}{cos^2(x^2)}cdot 2x\\\y=(frac{1}{sqrt{x^3}})^4+frac{3}{x^2}-5x\\y'=4(frac{1}{sqrt{x^3}})^3cdot frac{-frac{3}{2}cdot x^{frac{1}{2}}}{x^3}-frac{3cdot 2x}{x^4}-5=-frac{6}{x^7}-frac{6}{x^3}-5$

Answer 2

http://znanija.com/task/14840405