What is maclaurin tan(2x) ?

The answer to maclaurin tan(2x) is 2x+8/3 x^3+64/15 x^5+2176/315 x^7+31744/2835 x^9+\ldots

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maclaurin tan(2x)

maclaurin

tan (2 x)

2 x + \frac{8}{3} x^{3} + \frac{64}{15} x^{5} + \frac{2176}{315} x^{7} + \frac{31744}{2835} x^{9} + \dots

Solution steps

Apply the Maclaurin Formula

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

Evaluate Derivatives

= 0 + \frac{2}{1 !} x + \frac{0}{2 !} x^{2} + \frac{16}{3 !} x^{3} + \frac{0}{4 !} x^{4} + \frac{512}{5 !} x^{5} + \frac{0}{6 !} x^{6} + \frac{34816}{7 !} x^{7} + \frac{0}{8 !} x^{8} + \frac{4063232}{9 !} x^{9} + \dots

Refine

= 2 x + \frac{8}{3} x^{3} + \frac{64}{15} x^{5} + \frac{2176}{315} x^{7} + \frac{31744}{2835} x^{9} + \dots

What is maclaurin tan(2x) ?
The answer to maclaurin tan(2x) is 2x+8/3 x^3+64/15 x^5+2176/315 x^7+31744/2835 x^9+\ldots