taylor (3/2)^x

Lösung

taylor

(\frac{3}{2})^{x}

1 + ln (\frac{3}{2}) x + \frac{ln ^{2} ( \frac{3}{2} )}{2} x^{2} + \frac{ln ^{3} ( \frac{3}{2} )}{6} x^{3} + \frac{ln ^{4} ( \frac{3}{2} )}{24} x^{4} + \dots

Schritte zur Lösung

Apply the Taylor Formula

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

Evaluate Derivatives

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

Fasse zusammen

= 1 + ln (\frac{3}{2}) x + \frac{ln ^{2} ( \frac{3}{2} )}{2} x^{2} + \frac{ln ^{3} ( \frac{3}{2} )}{6} x^{3} + \frac{ln ^{4} ( \frac{3}{2} )}{24} x^{4} + \dots

y^{^{''}} - 4 y^{^{'}} + 2 y = 0, y (0) = 0, y^{^{'}} (0) = 1

\frac{\partial}{\partial y} (4 e^{x} ln (y))

\frac{d}{d x} (x - \frac{1}{x})

\frac{d y}{d x} = e^{4 x - y}

\frac{d}{d x} (- x^{4})