Question

Найдите производную функции
$y=frac{x^9}{9}+ sqrt{2cosx}+tg frac{pi} {4}-2x^4$

Answer 1

$y = frac{x^9}9 + sqrt{2cosx} + tgfracpi4 - 2x^4\y' = (frac{x^9}9)' + (sqrt{2cosx})' + (tgfracpi4)' - (2x^4)'\(x^n)' = nx^{n-1}*x'; (sqrt x)' = frac{x'}{2sqrt x}; (tgx)' = frac{x'}{cos^2x}\y' = x^8 + frac{sqrt2}{2sqrt{cosx}} + frac1{cos^2fracpi4} - 8x^3$

Answer 2

$y=frac{x^9}{9}+sqrt{2}cos^{0,5}x+tg frac{pi} {4}-2x^4;\y'=frac{9}{9}x^8-frac{sqrt{2}sinx}{2cos^{0,5}x}+0-2*4x^3=\=x^8-frac{sinx}{sqrt{2cosx}}-8x^3$