derivative of x^5sqrt(x)

Lösung

\frac{d}{d x} (x^{5} x)

\frac{11 x ^{\frac{9}{2}}}{2}

Schritte zur Lösung

\frac{d}{d x} (x^{5} x)

Vereinfache

x^{5} x : x^{\frac{11}{2}}

= \frac{d}{d x} (x^{\frac{11}{2}})

Wende die Potenzregel an:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= \frac{11}{2} x^{\frac{11}{2} - 1}

Vereinfache

\frac{11}{2} x^{\frac{11}{2} - 1} : \frac{11 x ^{\frac{9}{2}}}{2}

= \frac{11 x ^{\frac{9}{2}}}{2}

d er i v a t i v e f (x) = 3 x - 4

\int_{- \infty}^{1} e^{4 x} d x

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

n = 2 \sum \infty \frac{9}{n ( n + 2 )}

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