What is maclaurin 1/((1-3*x^3)^3) ?

The answer to maclaurin 1/((1-3*x^3)^3) is 1+9x^3+54x^6+270x^9+\ldots

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maclaurin 1/((1-3*x^3)^3)

maclaurin

\frac{1}{( 1 - 3 \cdot x ^{3} ) ^{3}}

1 + 9 x^{3} + 54 x^{6} + 270 x^{9} + \dots

Solution steps

Apply the Maclaurin Formula

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

Evaluate Derivatives

= 1 + \frac{0}{1 !} x + \frac{0}{2 !} x^{2} + \frac{54}{3 !} x^{3} + \frac{0}{4 !} x^{4} + \frac{0}{5 !} x^{5} + \frac{38880}{6 !} x^{6} + \frac{0}{7 !} x^{7} + \frac{0}{8 !} x^{8} + \frac{97977600}{9 !} x^{9} + \frac{0}{10 !} x^{10} + \dots

Refine

= 1 + 9 x^{3} + 54 x^{6} + 270 x^{9} + \dots

f (x) = 10 x, (10, 10)

\int \frac{x - 1}{x ^{2} - 4 x + 5} d x

\frac{d y}{d x} + y = - 1, y (0) = 1

2 x - 3

f (x) = 3 x + 4, at x = 4

What is maclaurin 1/((1-3*x^3)^3) ?
The answer to maclaurin 1/((1-3*x^3)^3) is 1+9x^3+54x^6+270x^9+\ldots