What is taylor (x^2+4)^{-3} ?

The answer to taylor (x^2+4)^{-3} is 1/64-3/256 x^2+3/512 x^4-5/2048 x^6+15/16384 x^8+\ldots

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taylor (x^2+4)^{-3}

taylor

(x^{2} + 4)^{- 3}

\frac{1}{64} - \frac{3}{256} x^{2} + \frac{3}{512} x^{4} - \frac{5}{2048} x^{6} + \frac{15}{16384} x^{8} + \dots

Solution steps

Apply the Taylor Formula

= \frac{1}{64} + \frac{\frac{d}{d x} ( ( x ^{2} + 4 ) ^{- 3} ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( ( x ^{2} + 4 ) ^{- 3} ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( ( x ^{2} + 4 ) ^{- 3} ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= \frac{1}{64} + \frac{0}{1 !} x + \frac{- \frac{3}{128}}{2 !} x^{2} + \frac{0}{3 !} x^{3} + \frac{\frac{9}{64}}{4 !} x^{4} + \frac{0}{5 !} x^{5} + \frac{- \frac{225}{128}}{6 !} x^{6} + \frac{0}{7 !} x^{7} + \frac{\frac{4725}{128}}{8 !} x^{8} + \dots

Refine

= \frac{1}{64} - \frac{3}{256} x^{2} + \frac{3}{512} x^{4} - \frac{5}{2048} x^{6} + \frac{15}{16384} x^{8} + \dots

\frac{\partial}{\partial y} (2 x^{3} + x^{2} y + 3 x y^{2})

y = x^{2} + 3

\int \frac{7 x}{e ^{x^{2}}} d x

\int \frac{1}{x ^{3}} + \frac{6}{x ^{7}} d x

n = 0 \sum \infty \frac{1}{( 2 + 2 n ) ^{3}}

What is taylor (x^2+4)^{-3} ?
The answer to taylor (x^2+4)^{-3} is 1/64-3/256 x^2+3/512 x^4-5/2048 x^6+15/16384 x^8+\ldots