What is taylor 1/((x^2+4)^3) ?

The answer to taylor 1/((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 1/((x^2+4)^3)

taylor

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

x \to 10 lim (5)

y^{^{''}} - 11 y^{^{'}} + 24 y = e^{- 4 t}

\frac{d}{d x} ((4 x - 3)^{\frac{1}{3}})

\frac{\partial}{\partial x} (\frac{1}{( 1 + x ) ^{2}})

\frac{d}{d x} (\frac{x ∣ x ∣}{2})

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