derivative of 5sqrt((xy/2))

Lösung

\frac{d}{d x} (5 \frac{x y}{2})

\frac{5 ( y + x \frac{d y}{d x} )}{2 2 x y}

Schritte zur Lösung

\frac{d}{d x} (5 \frac{x y}{2})

Entferne die Konstante:

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

= 5 \frac{d}{d x} (\frac{x y}{2})

Wende die Kettenregel an:

\frac{1}{2 \frac{x y}{2}} \frac{d}{d x} (\frac{x y}{2})

= \frac{1}{2 \frac{x y}{2}} \frac{d}{d x} (\frac{x y}{2})

\frac{d}{d x} (\frac{x y}{2}) = \frac{1}{2} (y + x \frac{d y}{d x})

= 5 \cdot \frac{1}{2 \frac{x y}{2}} \cdot \frac{1}{2} (y + x \frac{d y}{d x})

Vereinfache

5 \cdot \frac{1}{2 \frac{x y}{2}} \cdot \frac{1}{2} (y + x \frac{d y}{d x}) : \frac{5 ( y + x \frac{d y}{d x} )}{2 2 x y}

= \frac{5 ( y + x \frac{d y}{d x} )}{2 2 x y}

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

d er i v a t i v e arccos (x^{\frac{1}{2}})

d er i v a t i v e 4 x^{3} + e^{16 x} - 3^{2 x - 1}

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

\int 4 3 y + 1 d y