show steps y x1ex fr rer 1 r2Solutiony x1ex use uv rule du

Solution

y= (x+1)e^x

use uv rule

d(uv) = u dv + v du

y\' = dy/dx = (x+1) e^x + e^x *1 = (x+2) e^x

f(r)= re^r / 1 + r^2

use u/v rule

d(u/v) = v du - u dv / v^2

f\'(r) = (1+r^2) (1+r) e^r - r e^r 2r / (1+r^2)^2

= ((1+r^2) (1+r) e^r - 2r^2 e^r)/ (1+r^2)^2