partial derivative
- noun
- /ˈpɑrʧəl dɪˈrɪvətɪv/
- Specialized
:
derivada parcial
- Based on Equation 4, the net effect of the dataset's temporal range is calculated. The effect that time (in number of months) has on spatial statistics is given by the partial derivative of the spatial autocorrelation detection equation.
And you know, I thought partial derivatives should do the trick.
- And you know, I thought partial derivatives should do the trick.
- So this case the dot is a partial derivative with respect to time.
Examples
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Let's compute the partial derivative of F with respect to X.
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We're taking the partial derivative with respect to X.
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And now let's look at the partial derivative of a with respect to J.
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So the mixed partial derivative is just zero.
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It's a partial derivative with respect to its inputs.
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Here, Y is a function of S&T, hence the partial derivative notation.
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That is, we start by calculating the partial derivatives of F with respect to X for a particular t, then integrate these derivatives over the whole range of t.
Academic text (2001) -
To find the slope of the function at a specific point, we calculate the partial derivative with respect to x while keeping y constant.
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In multivariable calculus, understanding the concept of a partial derivative is crucial for analyzing functions of several variables.
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The partial derivative of z with respect to x indicates how z changes as x varies, while other variables are held constant.
Synonyms
3
9.3
A way to measure how a function changes when one variable changes and others stay the same
Surface Forms
Morphology
The phrase combines 'partial' (relating to a part or part of something) with 'derivative' (a rate of change), so it compositionally signals a derivative that applies to only part of the inputs — i.e., one variable. However, the precise technical meaning (differentiating with respect to one variable while keeping others constant) requires mathematical knowledge beyond the ordinary word senses, so the relation is not fully predictable to a general learner.
Etymology
Partial derivative comes from the idea of looking at only one part of a change. Imagine walking on a hill and measuring how steep it is when you move in one direction while keeping the other directions the same. The word partial means 'part' and derivative means 'rate of change', so a partial derivative shows 'how something changes' when only one variable moves.