Question

Найдите производную функции 1/3x^9+2/7x^49-5x+9+1/9x^81.помогите пожалуйста

Answer 1

y=1/(3*x^9)+2/(7*x^49)-5*x+9+1/(9*x^81)=1/3*x^-9+2/7*x^-49-5x+9+1/9*x^-81
y'= 1/3*(-9)*x^-10+2/7*(-49)*x^-50-5+1/9+(-81)*x^-82= -3*x^-10-14*x^-50-5-9*x^-82

Answer 2

$(\frac{1}{3} x^9+ \frac{2}{7} x^{49}-5x+9+ \frac{1}{9}x^{81})' = \\ \\ = (\frac{1}{3} x^9)' + (\frac{2}{7} x^{49})' - (5x)' + 9' + (\frac{1}{9}x^{81})' = \\ \\ = \frac{1}{3}*9* x^8 + \frac{2}{7} *49 * x^{48} - 5 + 0 + \frac{1}{9}* 81 * x^{80} = \\ \\ = 3x^8 + 14 x^{48} - 5 + {9}x^{80}$