What is taylor x*sec(x) ?

The answer to taylor x*sec(x) is x+1/2 x^3+5/24 x^5+61/720 x^7+\ldots

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taylor x*sec(x)

taylor

x \cdot sec (x)

x + \frac{1}{2} x^{3} + \frac{5}{24} x^{5} + \frac{61}{720} x^{7} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= 0 + \frac{1}{1 !} x + \frac{0}{2 !} x^{2} + \frac{3}{3 !} x^{3} + \frac{0}{4 !} x^{4} + \frac{25}{5 !} x^{5} + \frac{0}{6 !} x^{6} + \frac{427}{7 !} x^{7} + \dots

Refine

= x + \frac{1}{2} x^{3} + \frac{5}{24} x^{5} + \frac{61}{720} x^{7} + \dots

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What is taylor x*sec(x) ?
The answer to taylor x*sec(x) is x+1/2 x^3+5/24 x^5+61/720 x^7+\ldots