derivative of x^{2y}

Lösung

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

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})

\int ((3 x - 4) e^{- x}) d x

t an g e n t f (x) = \frac{8}{x ^{2} + 4}, at x = 3

\int_{0}^{5} 5 x - x^{2} d x

\frac{d}{d x} (y^{4} - 2 x)

\frac{\partial}{\partial z} (x y^{2})