derivative of (7e^xx^{5/2}/2+e^xx^{7/2})

Lösung

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

\frac{28 e ^{x} x ^{\frac{5}{2}} + 35 e ^{x} x ^{\frac{3}{2}} + 4 e ^{x} x ^{\frac{7}{2}}}{4}

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

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

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

\frac{d}{d x} (\frac{7 e ^{x} x ^{\frac{5}{2}}}{2}) = \frac{7}{2} (e^{x} x^{\frac{5}{2}} + \frac{5 e ^{x} x ^{\frac{3}{2}}}{2})

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

= \frac{7}{2} (e^{x} x^{\frac{5}{2}} + \frac{5 e ^{x} x ^{\frac{3}{2}}}{2}) + e^{x} x^{\frac{7}{2}} + \frac{7 e ^{x} x ^{\frac{5}{2}}}{2}

Vereinfache

\frac{7}{2} (e^{x} x^{\frac{5}{2}} + \frac{5 e ^{x} x ^{\frac{3}{2}}}{2}) + e^{x} x^{\frac{7}{2}} + \frac{7 e ^{x} x ^{\frac{5}{2}}}{2} : \frac{28 e ^{x} x ^{\frac{5}{2}} + 35 e ^{x} x ^{\frac{3}{2}} + 4 e ^{x} x ^{\frac{7}{2}}}{4}

= \frac{28 e ^{x} x ^{\frac{5}{2}} + 35 e ^{x} x ^{\frac{3}{2}} + 4 e ^{x} x ^{\frac{7}{2}}}{4}

\frac{\partial}{\partial x} (x y^{3})

\int_{0}^{1} \frac{x ^{3}}{x ^{2} - x - 6} d x

in v erse l a pl a ce \frac{1}{s ^{2} + 40 s + 2000}

8 t^{2} y^{^{''}} - 16 y = 11 t^{2} - 1

d er i v a t i v e cot (3 x)