differential
differential — noun
1. the measured gap separating two amounts, values, or groups — such as the differe
the measured gap separating two amounts, values, or groups — such as the difference in pay between workers in different roles, or the price gap between two competing products.
The wage differential between nurses and doctors has been a topic of debate for years.
collocation: wage differential
Sahil decided to switch suppliers after seeing the price differential of nearly twenty percent.
collocation: price differential
A growing differential in living costs between the city and the countryside is pushing families to move further out.
The report revealed a clear differential in scores between tutored students and the rest.
文法句型
differential + between + noun + and + noun
differential + in + noun
用法筆記
Common in economic and business contexts. The noun usually appears with a modifier specifying what kind of gap is being measured (wage differential, price differential, age differential).
常見錯誤
2. a part of a vehicle's transmission system that lets the drive wheels spin at sep
a part of a vehicle's transmission system that lets the drive wheels spin at separate speeds, helping the car turn corners smoothly without skidding.
The mechanic said the differential needed a fluid change after sixty thousand kilometres.
collocation: differential + fluid change
Hao heard a grinding noise from the rear of the truck and suspected the differential was failing.
When a car turns, the differential allows the outer wheel to rotate faster than the inner wheel.
A broken differential can lock the rear wheels and make the car unsafe to drive.
- diff
informal shortening used by mechanics and car enthusiasts
- differential gear
the full technical term; slightly more formal
用法筆記
Often shortened to 'diff' by mechanics and car enthusiasts. The full term 'differential gear' is also common in technical writing.
3. in calculus, a value that represents how fast one quantity is changing at a spec
in calculus, a value that represents how fast one quantity is changing at a specific point compared to another related quantity, obtained through the process of differentiation.
In class, the professor showed how to find the differential of the function f of x with respect to x.
pattern: differential + of + function + with respect to
Allison used the differential to estimate the change in balloon volume from a small radius increase.
The differential dy equals the derivative of the function multiplied by dx, forming the basis of linear approximation.
Ignacio computed the differential of displacement over time to find the instantaneous velocity.
- derivative
closely related but distinct; the derivative is a function, while the differential is a specific value or expression linked to an increment
- instantaneous rate of change
a conceptual description rather than a synonym; captures the same idea in words
文法句型
differential + of + noun + with respect to + noun
用法筆記
Nearly exclusive to mathematics and physics contexts. Learners at lower levels rarely encounter this sense — it is safely deferred to C2 or domain-specific study.
常見錯誤
differential — adjective
1. relating to or based on a distinction between people, groups, or situations — fo
relating to or based on a distinction between people, groups, or situations — for instance, applying different rates, rules, or treatment depending on particular factors.
The company offers differential pricing for early bird customers and last-minute buyers.
collocation: differential pricing
Nkechi argued that differential treatment of employees based on gender is both unfair and illegal.
collocation: differential treatment
The new tax plan introduces differential rates for small businesses and large corporations.
Mayumi noticed a differential grading style between the two professors — one was generous, the other strict.
- discriminatory
negative connotation; implies unfair bias rather than neutral distinction
- distinguishing
focuses on the act of telling things apart rather than on the resulting difference
- differential (本身)
more neutral and technical than 'discriminatory'
文法句型
differential + noun
用法筆記
Almost always used before a noun (attributive). You cannot say 'This treatment is differential' in natural English; instead say 'This is differential treatment.'
常見錯誤
2. connected with the branch of mathematics that examines rates of change and slope
connected with the branch of mathematics that examines rates of change and slopes of curves — specifically, involving derivatives or the operation of differentiation.
Differential calculus is the foundation for understanding how objects move and change in physics.
compound noun: differential calculus
The engineering students spent the semester solving first-order differential equations.
compound noun: differential equation
Élise chose to write her thesis on differential geometry and its applications in robotics.
The team used a differential equation to model the growth of a bacterial population over time.
- integral
relating to integration, the inverse operation of differentiation in calculus
文法句型
differential + noun
用法筆記
This sense is almost entirely restricted to fixed compound terms in mathematics and physics: differential calculus, differential equation, differential geometry. Learners are best served by learning those compounds as whole units.