Product rule
Differentiate a product of a linear and a quadratic factor using the product rule. Unlimited questions, five difficulty levels, and a full worked solution every time — free.
Try one
Differentiate f(x) using the product rule.
f(x) = (−3x + 4)(x2 - 2)
- −6x
- −6x2 + 8x
- −9x2 + 8x + 6
- −3x2 + 6
Answer: -9x^2 + 8x + 6
See one solved, step by step
Differentiate f(x) using the product rule.
f(x) = (2x - 2)(2x2 + 5)
- 8x2 - 8x
- 12x2 - 8x + 10
- 4x2 + 10
- 8x
📘 Worked solution
1u = 2x - 2, u' = 2; v = 2x2 + 5, v' = 4xDifferentiate each factor separately first.
2f'(x) = u'v + uv' = 2(2x2 + 5) + (2x - 2)(4x)The product rule keeps both pieces: derivative of the first times the second, plus the first times the derivative of the second.
3= 12x2 - 8x + 10Expand and collect like terms.
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