What is maclaurin sin^2(3x) ?

The answer to maclaurin sin^2(3x) is 9x^2-27x^4+162/5 x^6-729/35 x^8+1458/175 x^{10}+\ldots

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maclaurin sin^2(3x)

maclaurin

sin^{2} (3 x)

9 x^{2} - 27 x^{4} + \frac{162}{5} x^{6} - \frac{729}{35} x^{8} + \frac{1458}{175} x^{10} + \dots

Solution steps

Apply the Maclaurin Formula

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

Evaluate Derivatives

= 0 + \frac{0}{1 !} x + \frac{18}{2 !} x^{2} + \frac{0}{3 !} x^{3} + \frac{- 648}{4 !} x^{4} + \frac{0}{5 !} x^{5} + \frac{23328}{6 !} x^{6} + \frac{0}{7 !} x^{7} + \frac{- 839808}{8 !} x^{8} + \frac{0}{9 !} x^{9} + \frac{30233088}{10 !} x^{10} + \dots

Refine

= 9 x^{2} - 27 x^{4} + \frac{162}{5} x^{6} - \frac{729}{35} x^{8} + \frac{1458}{175} x^{10} + \dots

t \to 1 lim (ln (t))

\frac{\partial}{\partial y} (x e^{y} + cos (y))

\frac{\partial}{\partial y} (\frac{3 x ^{2}}{y})

x \to 5 + lim (\frac{1}{( x - 5 ) ^{2}})

f (x) = \frac{1 + x}{1 - x}

What is maclaurin sin^2(3x) ?
The answer to maclaurin sin^2(3x) is 9x^2-27x^4+162/5 x^6-729/35 x^8+1458/175 x^{10}+\ldots