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Beliebt Rechnen >

derivative of x^{2y}

Lösung

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

Lösung

2 x^{2 y} (ln (x) \frac{d y}{d x} + \frac{y}{x})

Schritte zur Lösung

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

Wende Exponentenregel an:

a^{b} = e^{b l n (a)}

x^{2 y} = e^{2 y l n (x)}

= \frac{d}{d x} (e^{2 y l n (x)})

Wende die Kettenregel an:

e^{2 y l n (x)} \frac{d}{d x} (2 y ln (x))

= e^{2 y l n (x)} \frac{d}{d x} (2 y ln (x))

\frac{d}{d x} (2 y ln (x)) = 2 (ln (x) \frac{d y}{d x} + \frac{y}{x})

= e^{2 y l n (x)} \cdot 2 (ln (x) \frac{d y}{d x} + \frac{y}{x})

e^{2 y l n (x)} = x^{2 y}

= 2 x^{2 y} (ln (x) \frac{d y}{d x} + \frac{y}{x})

Beliebte Beispiele

integral of ((3x-4)e^{-x})

tangent f(x)= 8/(x^2+4),\at x=3

integral from 0 to 5 of 5x-x^2

derivative of y^4-2x

(\partial)/(\partial z)(xy^2)