What is maclaurin 6sin(5x) ?

The answer to maclaurin 6sin(5x) is 30x-125x^3+625/4 x^5-15625/168 x^7+390625/12096 x^9+\ldots

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maclaurin 6sin(5x)

maclaurin

6 sin (5 x)

30 x - 125 x^{3} + \frac{625}{4} x^{5} - \frac{15625}{168} x^{7} + \frac{390625}{12096} x^{9} + \dots

Solution steps

Apply the Maclaurin Formula

= 0 + \frac{\frac{d}{d x} ( 6 sin ( 5 x ) ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( 6 sin ( 5 x ) ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( 6 sin ( 5 x ) ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= 0 + \frac{30}{1 !} x + \frac{0}{2 !} x^{2} + \frac{- 750}{3 !} x^{3} + \frac{0}{4 !} x^{4} + \frac{18750}{5 !} x^{5} + \frac{0}{6 !} x^{6} + \frac{- 468750}{7 !} x^{7} + \frac{0}{8 !} x^{8} + \frac{11718750}{9 !} x^{9} + \dots

Refine

= 30 x - 125 x^{3} + \frac{625}{4} x^{5} - \frac{15625}{168} x^{7} + \frac{390625}{12096} x^{9} + \dots

What is maclaurin 6sin(5x) ?
The answer to maclaurin 6sin(5x) is 30x-125x^3+625/4 x^5-15625/168 x^7+390625/12096 x^9+\ldots