derivative of (x^2-5/4 e^x)

Lösung

\frac{d}{d x} ((x^{2} - \frac{5}{4}) e^{x})

2 x e^{x} + e^{x} (x^{2} - \frac{5}{4})

Schritte zur Lösung

\frac{d}{d x} ((x^{2} - \frac{5}{4}) e^{x})

Wende die Produktregel an:

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

f = x^{2} - \frac{5}{4}, g = e^{x}

= \frac{d}{d x} (x^{2} - \frac{5}{4}) e^{x} + \frac{d}{d x} (e^{x}) (x^{2} - \frac{5}{4})

\frac{d}{d x} (x^{2} - \frac{5}{4}) = 2 x

\frac{d}{d x} (e^{x}) = e^{x}

= 2 x e^{x} + e^{x} (x^{2} - \frac{5}{4})

\int \frac{3 x}{x ^{2} - 2} d x

im pl i c i t \frac{d y}{d x}, (cos (π x) + sin (π y))^{5} = 23

n = 1 \sum \infty r^{n}

\frac{\partial}{\partial y} (x^{2} e^{yz})

\frac{d}{d x} (x^{2} + \frac{cos ( x )}{2})