Calculus Question

Question

Find dy/dx given y=(4+xe^x)/e^x

Answer 1

Hi Yorke, you can apply either the product rule or division rule of derivatives to solve this problem. Let's apply product rule:

y = (4+xe^x)/e^x = (4+xe^x)*e^-x

The product rule of differentiation is: if f = uv, then f' = uv' + vu'

let u = 4 + xe^x, v = e^-x

y' = (4+xe^x)*(-e^-x) + e^-x * (xe^x + e^x)

= -(4+xe^x)/e^x + x + 1

= -4/e^x - x + x + 1

= 1 - 4e^-x

Hope this helps!