What is taylor ln(cos(x)+sin(x)) ?

The answer to taylor ln(cos(x)+sin(x)) is x-x^2+2/3 x^3-2/3 x^4+2/3 x^5+\ldots

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taylor ln(cos(x)+sin(x))

taylor

ln (cos (x) + sin (x))

x - x^{2} + \frac{2}{3} x^{3} - \frac{2}{3} x^{4} + \frac{2}{3} x^{5} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= 0 + \frac{1}{1 !} x + \frac{- 2}{2 !} x^{2} + \frac{4}{3 !} x^{3} + \frac{- 16}{4 !} x^{4} + \frac{80}{5 !} x^{5} + \dots

Refine

= x - x^{2} + \frac{2}{3} x^{3} - \frac{2}{3} x^{4} + \frac{2}{3} x^{5} + \dots

d er i v a t i v e e^{x} (x + 1)

\int e^{- 5} d x

\frac{d}{d x} (x^{2} - y^{2})

\int \frac{2}{2 x - 3} d x

\frac{d y}{d x} = 2 y + x^{2} + 5

What is taylor ln(cos(x)+sin(x)) ?
The answer to taylor ln(cos(x)+sin(x)) is x-x^2+2/3 x^3-2/3 x^4+2/3 x^5+\ldots