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

Lösung

ableitung von

\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}

d er i v a t i v e y = 5 cos^{2} (π x)

\frac{d}{d x} (ln (2 x + 3 y))

(2 x^{2} y + 2 y + 5) d x + (2 x^{3} + 2 x) d y = 0

\int e^{- a x} x d x

d er i v a t i v e f (x) = \frac{3 x}{7 x ^{2} + 1}