What is taylor 4ln(7+2x^2) ?

The answer to taylor 4ln(7+2x^2) is 4ln(7)+8/7 x^2-8/49 x^4+32/1029 x^6-16/2401 x^8+\ldots

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taylor 4ln(7+2x^2)

taylor

4 ln (7 + 2 x^{2})

4 ln (7) + \frac{8}{7} x^{2} - \frac{8}{49} x^{4} + \frac{32}{1029} x^{6} - \frac{16}{2401} x^{8} + \dots

Solution steps

Apply the Taylor Formula

= 4 ln (7) + \frac{\frac{d}{d x} ( 4 ln ( 7 + 2 x ^{2} ) ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( 4 ln ( 7 + 2 x ^{2} ) ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( 4 ln ( 7 + 2 x ^{2} ) ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= 4 ln (7) + \frac{0}{1 !} x + \frac{\frac{16}{7}}{2 !} x^{2} + \frac{0}{3 !} x^{3} + \frac{- \frac{192}{49}}{4 !} x^{4} + \frac{0}{5 !} x^{5} + \frac{\frac{7680}{343}}{6 !} x^{6} + \frac{0}{7 !} x^{7} + \frac{- \frac{92160}{343}}{8 !} x^{8} + \dots

Refine

= 4 ln (7) + \frac{8}{7} x^{2} - \frac{8}{49} x^{4} + \frac{32}{1029} x^{6} - \frac{16}{2401} x^{8} + \dots

f (x) = \frac{1}{x ^{6}}

sec (x) - 6 cos (x)

\frac{\partial}{\partial y} (x^{y} - x y)

\frac{d y}{d x} = 2 x e^{y}

\frac{d}{d x} ((3 x)^{3 x})

What is taylor 4ln(7+2x^2) ?
The answer to taylor 4ln(7+2x^2) is 4ln(7)+8/7 x^2-8/49 x^4+32/1029 x^6-16/2401 x^8+\ldots