What is taylor 3/((3+(x+2)^2)^{3/2)},0 ?

The answer to taylor 3/((3+(x+2)^2)^{3/2)},0 is

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taylor 3/((3+(x+2)^2)^{3/2)},0

taylor

\frac{3}{( 3 + ( x + 2 ) ^{2} ) ^{\frac{3}{2}}}, 0

\frac{3}{7 \cdot 7 ^{\frac{1}{2}}} - \frac{18}{49 \cdot 7 ^{\frac{1}{2}}} x + \frac{117}{686 \cdot 7 ^{\frac{1}{2}}} x^{2} - \frac{15}{343 \cdot 7 ^{\frac{1}{2}}} x^{3} - \frac{45}{19208 \cdot 7 ^{\frac{1}{2}}} x^{4} + \dots

Solution steps

Apply the Taylor Formula

= \frac{3}{7 \cdot 7 ^{\frac{1}{2}}} + \frac{\frac{d}{d x} ( \frac{3}{( 3 + ( x + 2 ) ^{2} ) ^{\frac{3}{2}}} ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( \frac{3}{( 3 + ( x + 2 ) ^{2} ) ^{\frac{3}{2}}} ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( \frac{3}{( 3 + ( x + 2 ) ^{2} ) ^{\frac{3}{2}}} ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= \frac{3}{7 \cdot 7 ^{\frac{1}{2}}} + \frac{- \frac{18}{49 \cdot 7 ^{\frac{1}{2}}}}{1 !} x + \frac{\frac{117}{343 \cdot 7 ^{\frac{1}{2}}}}{2 !} x^{2} + \frac{- \frac{90}{343 \cdot 7 ^{\frac{1}{2}}}}{3 !} x^{3} + \frac{- \frac{135}{2401 \cdot 7 ^{\frac{1}{2}}}}{4 !} x^{4} + \dots

Refine

= \frac{3}{7 \cdot 7 ^{\frac{1}{2}}} - \frac{18}{49 \cdot 7 ^{\frac{1}{2}}} x + \frac{117}{686 \cdot 7 ^{\frac{1}{2}}} x^{2} - \frac{15}{343 \cdot 7 ^{\frac{1}{2}}} x^{3} - \frac{45}{19208 \cdot 7 ^{\frac{1}{2}}} x^{4} + \dots

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What is taylor 3/((3+(x+2)^2)^{3/2)},0 ?
The answer to taylor 3/((3+(x+2)^2)^{3/2)},0 is