Find the derivative of f(x) = x³ * sin(x) using the product rule.

Mathematics

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Graph of f(x) = x³sin(x)

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Key points of f(x) = x³sin(x)
Pointxy
x-intercept−6.280
Minimum−5.23−124.32
x-intercept−3.140
Maximum−2.469.38
y-intercept00
Maximum2.469.38
x-intercept3.140
Minimum5.23−124.32
x-intercept6.280

The derivative of f(x)=x3sin⁡(x)f(x) = x^3 \sin(x) using the product rule is f′(x)=3x2sin⁡(x)+x3cos⁡(x)f'(x) = 3x^2 \sin(x) + x^3 \cos(x).

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