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

The answer to taylor (1+x^2)^{3/2}x is x+3/2 x^3+3/8 x^5-1/16 x^7+3/128 x^9+\ldots

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

taylor

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

x + \frac{3}{2} x^{3} + \frac{3}{8} x^{5} - \frac{1}{16} x^{7} + \frac{3}{128} x^{9} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= 0 + \frac{1}{1 !} x + \frac{0}{2 !} x^{2} + \frac{9}{3 !} x^{3} + \frac{0}{4 !} x^{4} + \frac{45}{5 !} x^{5} + \frac{0}{6 !} x^{6} + \frac{- 315}{7 !} x^{7} + \frac{0}{8 !} x^{8} + \frac{8505}{9 !} x^{9} + \dots

Refine

= x + \frac{3}{2} x^{3} + \frac{3}{8} x^{5} - \frac{1}{16} x^{7} + \frac{3}{128} x^{9} + \dots

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What is taylor (1+x^2)^{3/2}x ?
The answer to taylor (1+x^2)^{3/2}x is x+3/2 x^3+3/8 x^5-1/16 x^7+3/128 x^9+\ldots