What is taylor e^x-e^{-x} ?

The answer to taylor e^x-e^{-x} is 2x+1/3 x^3+1/60 x^5+1/2520 x^7+1/181440 x^9+\ldots

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taylor e^x-e^{-x}

taylor

e^{x} - e^{- x}

2 x + \frac{1}{3} x^{3} + \frac{1}{60} x^{5} + \frac{1}{2520} x^{7} + \frac{1}{181440} x^{9} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

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

Refine

= 2 x + \frac{1}{3} x^{3} + \frac{1}{60} x^{5} + \frac{1}{2520} x^{7} + \frac{1}{181440} x^{9} + \dots

\frac{d}{d x} (e^{5 x y})

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\frac{\partial}{\partial θ} (z)

\frac{d}{d x} ((2 x - 5)^{- 1} \cdot (4 x + 3)^{- 1})

\int_{0}^{3} \frac{9 e ^{9 x}}{1 + e ^{9 x}} d x

What is taylor e^x-e^{-x} ?
The answer to taylor e^x-e^{-x} is 2x+1/3 x^3+1/60 x^5+1/2520 x^7+1/181440 x^9+\ldots