derivative of xe^{x^2-y}

Lösung

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

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

Schritte zur Lösung

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

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = e^{x^{2} - y}

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

\frac{d x}{d x} = 1

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

= 1 \cdot e^{x^{2} - y} + e^{x^{2} - y} (2 x - \frac{d y}{d x}) x

Vereinfache

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

d er i v a t i v e (1 + t) (2 t^{2} - 7)

\int \frac{4}{1 - x ^{2}} d x

d er i v a t i v e sin (3 ln (x))

\frac{\partial}{\partial x} (3 ln (x + y) - 3 x)

d er i v a t i v e π t + cos (\frac{4 π t + π}{2})