Question

НАЙТИ ПРОИЗВОДНУЮ ФУНКЦИИ.
Помогите пожалуйста..... :(((

Answer 1

7) y=x⁷⁰*sin(x)

y'=(x⁷⁰)'*sin(x)+x⁷⁰*(sin(x))'=70*x⁶⁹*sin(x)+x⁷⁰*cos(x)=

=x⁶⁹*(70*sin(x)+x*cos(x)).

8) y=(x⁵-1)/(x⁶+1)

y'=((x⁵-1)'*(x⁶+1)-(x⁵-1)*(x⁶+1))/(x⁶+1)²=(5x⁴*(x⁶+1)-6x⁵*(5x-1))/(x⁶-1)²=

=(x⁴*(5*(x⁶+1)-6x*(x⁵-1))/(x⁶+1)²=x⁴*(5x⁶+5-6x⁶+6x)/(x⁶+1)²=

=x⁴*(-x⁶+6x+5)/(x⁶+1)².

Answer 2

$7)\;\;y = x^{70}sinx\\\\y' = (x^{70})'sinx + x^{70}(sinx)' = 70x^{69}sinx + x^{70}cosx = x^{69}(70sinx+xcosx)\\\\8) \;\; y = \frac{x^5-1}{x^6+1}\\\\y' \!= \frac{(x^5-1)'(x^6+1)-(x^5-1)(x^6+1)'}{(x^6+1)^2} = \frac{5x^4(x^6+1)-6x^5(x^5-1)}{(x^6+1)^2} = \frac{5x^{10}+5x^4-6x^{10}+6x^5}{(x^6+1)^2} = \\\\ = \frac{-x^{10}+6x^5+5x^4}{(x^6+1)^2} = \frac{x^4(-x^{6}+6x+5)}{(x^6+1)^2}$