What is maclaurin 6ln(9-x) ?

The answer to maclaurin 6ln(9-x) is 12ln(3)-2/3 x-1/27 x^2-2/729 x^3-1/4374 x^4+\ldots

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maclaurin 6ln(9-x)

maclaurin

6 ln (9 - x)

12 ln (3) - \frac{2}{3} x - \frac{1}{27} x^{2} - \frac{2}{729} x^{3} - \frac{1}{4374} x^{4} + \dots

Solution steps

Apply the Maclaurin Formula

= 12 ln (3) + \frac{\frac{d}{d x} ( 6 ln ( 9 - x ) ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( 6 ln ( 9 - x ) ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( 6 ln ( 9 - x ) ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= 12 ln (3) + \frac{- \frac{2}{3}}{1 !} x + \frac{- \frac{2}{27}}{2 !} x^{2} + \frac{- \frac{4}{243}}{3 !} x^{3} + \frac{- \frac{4}{729}}{4 !} x^{4} + \dots

Refine

= 12 ln (3) - \frac{2}{3} x - \frac{1}{27} x^{2} - \frac{2}{729} x^{3} - \frac{1}{4374} x^{4} + \dots

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What is maclaurin 6ln(9-x) ?
The answer to maclaurin 6ln(9-x) is 12ln(3)-2/3 x-1/27 x^2-2/729 x^3-1/4374 x^4+\ldots