What is taylor cos(x-7x) ?

The answer to taylor cos(x-7x) is 1-18x^2+54x^4-324/5 x^6+1458/35 x^8+\ldots

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taylor cos(x-7x)

taylor

cos (x - 7 x)

1 - 18 x^{2} + 54 x^{4} - \frac{324}{5} x^{6} + \frac{1458}{35} x^{8} + \dots

Solution steps

Apply the Taylor Formula

= 1 + \frac{\frac{d}{d x} ( cos ( x - 7 x ) ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( cos ( x - 7 x ) ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( cos ( x - 7 x ) ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= 1 + \frac{0}{1 !} x + \frac{- 36}{2 !} x^{2} + \frac{0}{3 !} x^{3} + \frac{1296}{4 !} x^{4} + \frac{0}{5 !} x^{5} + \frac{- 46656}{6 !} x^{6} + \frac{0}{7 !} x^{7} + \frac{1679616}{8 !} x^{8} + \dots

Refine

= 1 - 18 x^{2} + 54 x^{4} - \frac{324}{5} x^{6} + \frac{1458}{35} x^{8} + \dots

What is taylor cos(x-7x) ?
The answer to taylor cos(x-7x) is 1-18x^2+54x^4-324/5 x^6+1458/35 x^8+\ldots