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

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.

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If f(x) = x3 sin ⁡x, then 𝑑⁢𝑓𝑑⁢𝑥 is ______.

Question

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

Options

3x² + cos⁡ x
x³ cos x − 3x² sin x
x³ cos x + 3x² sin x
3x² cos x

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Solution

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.