derivative of y=ln(10x^2-8)

Lösung

\frac{d}{d x} y = ln (10 x^{2} - 8)

y = x ln (10 x^{2} - 8) - 2 x + \frac{2}{5} ln (\frac{5}{2} x + 1) - \frac{2}{5} ln (\frac{5}{2} x - 1) + c_{1}

Schritte zur Lösung

\frac{d y}{d x} = ln (10 x^{2} - 8)

Wenn

f^{^{'}} (x) = g (x)

dann

f (x) = \int g (x) d x

y = \int ln (10 x^{2} - 8) d x

\int ln (10 x^{2} - 8) d x = x ln (10 x^{2} - 8) - 2 x + \frac{2}{5} ln (\frac{5}{2} x + 1) - \frac{2}{5} ln (\frac{5}{2} x - 1) + c_{1}

y = x ln (10 x^{2} - 8) - 2 x + \frac{2}{5} ln (\frac{5}{2} x + 1) - \frac{2}{5} ln (\frac{5}{2} x - 1) + c_{1}

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