Question

I want derivative for (x+1)^2×e^xplease help​

Answer 1

Answer:

(x + 1)(x + 3)eˣ

Step-by-step explanation:

Since f(x) = (x + 1)²eˣ

df(x)/dx = d[(x + 1)²eˣ]/dx

By the product rule, duv/dx = udv/dx + vdu/dx

where  u =  (x + 1)² and v = eˣ

So,  df(x)/dx = d[(x + 1)²eˣ]/dx

= (x + 1)²deˣ/dx + eˣd(x + 1)²/dx

= (x + 1)²eˣ + eˣd(x + 1)²/d(x + 1) × d(x + 1)/dx  (by the chain-rule dy/dx = dy/du × du/dx)

= (x + 1)²eˣ + eˣ[2(x + 1) × 1]

= (x + 1)²eˣ + 2eˣ(x + 1)

= (x + 1)eˣ(x + 1 + 2)

= (x + 1)eˣ(x + 3)

= (x + 1)(x + 3)eˣ