What is maclaurin arctan(4x) ?

The answer to maclaurin arctan(4x) is 4x-64/3 x^3+1024/5 x^5-16384/7 x^7+262144/9 x^9+\ldots

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maclaurin arctan(4x)

maclaurin

arctan (4 x)

4 x - \frac{64}{3} x^{3} + \frac{1024}{5} x^{5} - \frac{16384}{7} x^{7} + \frac{262144}{9} x^{9} + \dots

Solution steps

Apply the Maclaurin Formula

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

Evaluate Derivatives

= 0 + \frac{4}{1 !} x + \frac{0}{2 !} x^{2} + \frac{- 128}{3 !} x^{3} + \frac{0}{4 !} x^{4} + \frac{24576}{5 !} x^{5} + \frac{0}{6 !} x^{6} + \frac{- 11796480}{7 !} x^{7} + \frac{0}{8 !} x^{8} + \frac{10569646080}{9 !} x^{9} + \dots

Refine

= 4 x - \frac{64}{3} x^{3} + \frac{1024}{5} x^{5} - \frac{16384}{7} x^{7} + \frac{262144}{9} x^{9} + \dots

\frac{d}{d x} ((x^{- 2} + x)^{3} \cdot (4 x)^{- 2 x})

\frac{\partial}{\partial x} (l - c)

\int x (15 x + 4) d x

\frac{( 6 x ^{2} + 6 x + 4 )}{x}

\frac{d}{d x} (x y^{4})

What is maclaurin arctan(4x) ?
The answer to maclaurin arctan(4x) is 4x-64/3 x^3+1024/5 x^5-16384/7 x^7+262144/9 x^9+\ldots