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| Approximations by Differentials |
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| Let y = f (x) be a differentiable function of x, errors in x and y are denoted by dx and dy, we have |
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| \ Error in y = f ' (x) dx. |
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| Note 1: |
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| Note 2: |
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| Note 3: |
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| dy and dy are not usually the same and dy is the approximate value of dy. |
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| Note 4: dx and dy are called the differentials of x and y respectively. |
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| Example: |
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| Find the approximate value of fourth root of 82 upto 3 decimal places. |
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| Solution: |
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| Let y = f (x) = x1/4 |
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| Let x = 81, dx =1. Taking these values we have |
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Application of Derivatives
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