derivative of ((x^2+32x^{1/2})/8)

Lösung

\frac{d}{d x} \frac{( x ^{2} + 32 x ^{\frac{1}{2}} )}{8}

\frac{x ^{\frac{3}{2}} + 8}{4 x ^{\frac{1}{2}}}

Schritte zur Lösung

\frac{d}{d x} \frac{( x ^{2} + 32 x ^{\frac{1}{2}} )}{8}

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{1}{8} \frac{d}{d x} (x^{2} + 32 x^{\frac{1}{2}})

Wende die Summen-/Differenzregel an:

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

= \frac{1}{8} (\frac{d}{d x} (x^{2}) + \frac{d}{d x} (32 x^{\frac{1}{2}}))

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

\frac{d}{d x} (32 x^{\frac{1}{2}}) = \frac{16}{x ^{\frac{1}{2}}}

= \frac{1}{8} (2 x + \frac{16}{x ^{\frac{1}{2}}})

Vereinfache

\frac{1}{8} (2 x + \frac{16}{x ^{\frac{1}{2}}}) : \frac{x ^{\frac{3}{2}} + 8}{4 x ^{\frac{1}{2}}}

= \frac{x ^{\frac{3}{2}} + 8}{4 x ^{\frac{1}{2}}}

(e^{y} + 1)^{2} e^{- y} d x + (e^{x} + 1) e^{- x} d y = 0

t a y l or \frac{1}{( x - 1 ) ^{2}}

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

d er i v a t i v e \frac{x ^{3}}{3 - x ^{2}}

\int_{- 9}^{0} \frac{1}{( x - 9 ) ^{2}} d x