derivative of (9e^xx^{7/2}/2+e^xx^{9/2})

Lösung

\frac{d}{d x} (\frac{9 e ^{x} x ^{\frac{7}{2}}}{2} + e^{x} x^{\frac{9}{2}})

\frac{36 e ^{x} x ^{\frac{7}{2}} + 63 e ^{x} x ^{\frac{5}{2}} + 4 e ^{x} x ^{\frac{9}{2}}}{4}

Schritte zur Lösung

\frac{d}{d x} (\frac{9 e ^{x} x ^{\frac{7}{2}}}{2} + e^{x} x^{\frac{9}{2}})

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (\frac{9 e ^{x} x ^{\frac{7}{2}}}{2}) + \frac{d}{d x} (e^{x} x^{\frac{9}{2}})

\frac{d}{d x} (\frac{9 e ^{x} x ^{\frac{7}{2}}}{2}) = \frac{9}{2} (e^{x} x^{\frac{7}{2}} + \frac{7 e ^{x} x ^{\frac{5}{2}}}{2})

\frac{d}{d x} (e^{x} x^{\frac{9}{2}}) = e^{x} x^{\frac{9}{2}} + \frac{9 e ^{x} x ^{\frac{7}{2}}}{2}

= \frac{9}{2} (e^{x} x^{\frac{7}{2}} + \frac{7 e ^{x} x ^{\frac{5}{2}}}{2}) + e^{x} x^{\frac{9}{2}} + \frac{9 e ^{x} x ^{\frac{7}{2}}}{2}

Vereinfache

\frac{9}{2} (e^{x} x^{\frac{7}{2}} + \frac{7 e ^{x} x ^{\frac{5}{2}}}{2}) + e^{x} x^{\frac{9}{2}} + \frac{9 e ^{x} x ^{\frac{7}{2}}}{2} : \frac{36 e ^{x} x ^{\frac{7}{2}} + 63 e ^{x} x ^{\frac{5}{2}} + 4 e ^{x} x ^{\frac{9}{2}}}{4}

= \frac{36 e ^{x} x ^{\frac{7}{2}} + 63 e ^{x} x ^{\frac{5}{2}} + 4 e ^{x} x ^{\frac{9}{2}}}{4}

\frac{\partial}{\partial x} (\frac{4 x + 9}{3 y + 1})

d er i v a t i v e f (x) = 4 x^{2} + 5 x + 3

\int (x^{3} + 3 x)^{32} (3 x^{2} + 3) d x

x \to \infty lim (1 + \frac{1}{x})

d er i v a t i v e x x^{2} + 5