Quotient rule
Differentiate a ratio of two linear expressions using the quotient rule. Unlimited questions, five difficulty levels, and a full worked solution every time — free.
Try one
Differentiate f(x) using the quotient rule.
f(x) = (−2x + 4) / (3x + 2)
- 14/(3x + 2)2
- −16/(3x + 2)
- −16/(3x + 2)2
- 16/(3x + 2)2
Answer: -16/(3x + 2)^2
See one solved, step by step
Differentiate f(x) using the quotient rule.
f(x) = (−5x + 4) / (5x - 2)
- 10/(5x - 2)2
- 17/(5x - 2)2
- −10/(5x - 2)
- −10/(5x - 2)2
📘 Worked solution
1u = −5x + 4, u' = −5; v = 5x - 2, v' = 5Differentiate the top and bottom separately first.
2f'(x) = [-5(5x - 2) - 5(−5x + 4)] / (5x - 2)2Quotient rule: (derivative of top)(bottom) minus (top)(derivative of bottom), all over bottom squared.
3Numerator = −5·-2 - 4·5 = −10 (the x terms cancel)Expand the numerator — for two linear pieces the x^1 terms always cancel, leaving a constant.
4f'(x) = −10/(5x - 2)2Write the simplified numerator over the squared denominator.
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