derivative of (x-1*e^{x^2-4})

Lösung

\frac{d}{d x} ((x - 1) \cdot e^{x^{2} - 4})

e^{x^{2} - 4} + 2 e^{x^{2} - 4} x (x - 1)

Schritte zur Lösung

\frac{d}{d x} ((x - 1) e^{x^{2} - 4})

Wende die Produktregel an:

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

f = x - 1, g = e^{x^{2} - 4}

= \frac{d}{d x} (x - 1) e^{x^{2} - 4} + \frac{d}{d x} (e^{x^{2} - 4}) (x - 1)

\frac{d}{d x} (x - 1) = 1

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

= 1 \cdot e^{x^{2} - 4} + e^{x^{2} - 4} \cdot 2 x (x - 1)

Vereinfache

= e^{x^{2} - 4} + 2 e^{x^{2} - 4} x (x - 1)

\int x ln (a x) d x

\frac{d}{d x} (cos (x) cos (y))

\int_{1}^{4} \frac{x ^{2} + 2}{5 x - x ^{2}} d x

t an g e n t x (25.5)

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