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Beliebt Rechnen >

derivative y=x^7e^x

Lösung

ableitung von

y = x^{7} e^{x}

Lösung

7 x^{6} e^{x} + e^{x} x^{7}

Schritte zur Lösung

\frac{d}{d x} (x^{7} e^{x})

Wende die Produktregel an:

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

f = x^{7}, g = e^{x}

= \frac{d}{d x} (x^{7}) e^{x} + \frac{d}{d x} (e^{x}) x^{7}

\frac{d}{d x} (x^{7}) = 7 x^{6}

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

= 7 x^{6} e^{x} + e^{x} x^{7}

Graph

Beliebte Beispiele

integral of (-2)/(x^3)

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

integral from 1 to R of x^{-9/4}

\int_{1}^{R} x^{- \frac{9}{4}} d x

sum from n=1 to infinity of 1/(5^n+7)

n = 1 \sum \infty \frac{1}{5 ^{n} + 7}

x^2y^{''}+3xy^'=2

x^{2} y^{^{''}} + 3 x y^{^{'}} = 2

derivative of ln(8x^2+7x+2)

\frac{d}{d x} (ln (8 x^{2} + 7 x + 2))