Question

If f(x) = x³ sin ⁡x, then \[\frac {df}{dx}\] is ______.

पर्याय

•  3x² + cos⁡ x

• x³ cos x − 3x² sin x

• x³ cos x + 3x² sin x

• 3x² cos x

Answer 1

x³ cos x + 3x² sin x

Explanation:

Using the product rule \[\frac {d}{dx}\][f₁ ⋅ f₂] = f₁ \[\frac {df_2}{dx}\] + f₂ \[\frac {df_1}{dx}\]​​: here f₁ = x³ and f₂ = sin ⁡x, so the result is x³ cos⁡ x + 3x² sin ⁡x.