derivative of (x^3+1e^x)

Lösung

\frac{d}{d x} ((x^{3} + 1) e^{x})

3 x^{2} e^{x} + e^{x} (x^{3} + 1)

Schritte zur Lösung

\frac{d}{d x} ((x^{3} + 1) e^{x})

Wende die Produktregel an:

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

f = x^{3} + 1, g = e^{x}

= \frac{d}{d x} (x^{3} + 1) e^{x} + \frac{d}{d x} (e^{x}) (x^{3} + 1)

\frac{d}{d x} (x^{3} + 1) = 3 x^{2}

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

= 3 x^{2} e^{x} + e^{x} (x^{3} + 1)

\frac{d}{d x} (\frac{ln ( 7 x )}{7 x})

\int_{0}^{\infty} e^{- x} x^{2} d x

\int \frac{( x - 5 )}{x ^{2} - 18 x + 82} d x

d er i v a t i v e f (x) = 1.5 x^{2} + 2 x^{1.5}

n = 1 \sum \infty \frac{1}{n ^{4} + n ^{2}}