use the definition find derivative

Question

f(x)=(2x)/(3+x)

 

please explain by steps

Answer 1

Hello Karoulin,

 

This problem relates to finding derivative of the product (or ratio) of two functions:

 

f(x) = m(x)*n(x)

f(x)’ = m(x)*n(x)’ + n(x)*m(x)’

 

Therefore, pertinent to your problem definition:

 

f(x)’ = 2x* (-¹/_(x+3)²) + 2/(x+3) = 2/(x+3) - 2x/(x+3)² + 2/3

 

Hope this will help.