What is taylor 1/((x^2+25)^{-3)} ?

The answer to taylor 1/((x^2+25)^{-3)} is 15625+1875x^2+75x^4+x^6

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taylor 1/((x^2+25)^{-3)}

taylor

\frac{1}{( x ^{2} + 25 ) ^{- 3}}

15625 + 1875 x^{2} + 75 x^{4} + x^{6}

Solution steps

Apply the Taylor Formula

= 15625 + \frac{\frac{d}{d x} ( \frac{1}{( x ^{2} + 25 ) ^{- 3}} ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( \frac{1}{( x ^{2} + 25 ) ^{- 3}} ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( \frac{1}{( x ^{2} + 25 ) ^{- 3}} ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= 15625 + \frac{0}{1 !} x + \frac{3750}{2 !} x^{2} + \frac{0}{3 !} x^{3} + \frac{1800}{4 !} x^{4} + \frac{0}{5 !} x^{5} + \frac{720}{6 !} x^{6} + \frac{0}{7 !} x^{7} + \frac{0}{8 !} x^{8} + \frac{0}{9 !} x^{9} + \frac{0}{10 !} x^{10}

Refine

= 15625 + 1875 x^{2} + 75 x^{4} + x^{6}

y^{^{'}} + 20 y = 24

f (x) = (x^{5} - 2 x)^{2}

\int x^{2} - 9 d x

x \to 0 lim (\frac{x ^{2} - 5 x}{x})

\int 24 sin (x) d x

What is taylor 1/((x^2+25)^{-3)} ?
The answer to taylor 1/((x^2+25)^{-3)} is 15625+1875x^2+75x^4+x^6