Correct Answer - Option 2 : 3e

**Concept:**

**\(\rm \frac{\mathrm{d} (x^{n})}{\mathrm{d} x} = nx^{n-1}\)**

**\(\rm \frac{\mathrm{d} (uv)}{\mathrm{d} x} = u\frac{\mathrm{d} v}{\mathrm{d} x} + v \frac{\mathrm{d} u}{\mathrm{d} x}\)**

**\(\rm \frac{\mathrm{d} (e^{x})}{\mathrm{d} x} = e^{x}\)**

**Calculation:**

**Given: **f(x) = x2.ex

Now, f'(x) = **\(\rm \frac{\mathrm{d} (x^{2}e^{x})}{\mathrm{d} x}\)**

By chain rule ,

⇒ \(\rm \frac{\mathrm{d} (x^{2}e^{x})}{\mathrm{d} x} = e^{x}\frac{\mathrm{d} (x^{2})}{\mathrm{d} x} + x^{2} \frac{\mathrm{d} (e^{x})}{\mathrm{d} x}\)

= ex2x +x2 ex

= xe^{x}(x + 2)

At x = 1;

f'(x)|_{x=1} = 3e