What is taylor 9/(x^2),1 ?

The answer to taylor 9/(x^2),1 is 9-18(x-1)+27(x-1)^2-36(x-1)^3+45(x-1)^4+\ldots

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taylor 9/(x^2),1

taylor

\frac{9}{x ^{2}}, 1

9 - 18 (x - 1) + 27 (x - 1)^{2} - 36 (x - 1)^{3} + 45 (x - 1)^{4} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= 9 + \frac{- 18}{1 !} (x - 1) + \frac{54}{2 !} (x - 1)^{2} + \frac{- 216}{3 !} (x - 1)^{3} + \frac{1080}{4 !} (x - 1)^{4} + \dots

Refine

= 9 - 18 (x - 1) + 27 (x - 1)^{2} - 36 (x - 1)^{3} + 45 (x - 1)^{4} + \dots

\frac{e ^{x}}{2}, 0, 0, 2

\frac{\partial}{\partial y} (10 x^{9} y^{9} + 3)

\frac{\partial}{\partial y} (\frac{5}{y})

\frac{d}{d x} (\frac{\frac{d}{d x} ( sin ( x ) )}{x})

What is taylor 9/(x^2),1 ?
The answer to taylor 9/(x^2),1 is 9-18(x-1)+27(x-1)^2-36(x-1)^3+45(x-1)^4+\ldots