Question

найти производную функции y=(5+x)/(x-7)

Answer 1

y=(5+x)/(x-7)

y'=(5+x)'*(x-7)-(5+x)*(x-7)'/(x-7)^2

y'=(x-7)-(5+x)/(x-7)^2

y'=(x-7-5-x)/(x-7)^2

y'=-12/(x-7)^2

Answer 2

y=(5+x)/(x-7)

По  правилу    производная  дроби

 

y " =((5+x)(x-7) " = ((5+x) ' *(x-7)  -  (5+x)*(x-7) ' )/(x-7)^2 = ((1*(x-7) -1*(x+5))/(x-7)^2  =

 =(x-7-x-5)/(x-7)^2  =  -12)/(x-7)^2