Meaning & use
power of differential
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Meaning
phrasefixed phrasetechnicalmathematics
In calculus, the exponent written on a differential, such as the 2 in (dx)^2, showing repeated multiplication of the differential.
Grammar: Used as a noun phrase: 'the power of the differential dx is 2'. It often appears in discussions of higher-order differentials.
Patterns
- the power of the differential dx
- raise a differential to a power
- the nth power of a differential
In the expression (dx)^2, the power of the differential is 2.
The notation (dy)^3 indicates the third power of the differential dy.
When working with higher-order differentials, pay attention to the power of each differential.
Common combinations
- the nth power of a differential
- The general form (dx)^n shows the nth power of the differential dx.
- power of the differential
- In (dx)^2, the power of the differential is two.
- higher power of a differential
- Terms with a higher power of the differential are often neglected in approximations.
Synonyms and how they differ
- exponent of a differential
- This is a more general term; 'power of differential' specifically refers to the result of raising a differential to an exponent.
Word family
- differential noun
- An infinitesimal change in a variable, often written dx or dy.
- derivative noun
- The rate of change of a function, not to be confused with the power of a differential.
Commonly confused: power of differential or derivative of a power?
power of differential vs derivative of a power
This refers to finding the derivative of a function like x^n, which is n x^(n-1). 'Power of differential' is about the exponent on dx itself, not about differentiating a power function.
Practice
In the expression (dx)^3, what is the power of the differential?
Choose one answer.
The exponent written on dx is 3, so the power of the differential is 3. Option A would be correct for (dx)^1, and option B for (dx)^2. Option D is wrong because the power is clearly shown by the exponent.
Make it your own
Write a sentence using “power of differential”, then check it and compare it with the examples above.