derivative of xy^2-x^2y+xy

Lösung

\frac{d}{d x} (x y^{2} - x^{2} y + x y)

y^{2} + 2 x y \frac{d y}{d x} - 2 x y - x^{2} \frac{d y}{d x} + y + x \frac{d y}{d x}

Schritte zur Lösung

\frac{d}{d x} (x y^{2} - x^{2} y + x y)

Wende die Summen-/Differenzregel an:

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

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

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

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

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

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

Vereinfache

y^{2} + 2 x y \frac{d y}{d x} - (2 x y + \frac{d y}{d x} x^{2}) + y + x \frac{d y}{d x} : y^{2} + 2 x y \frac{d y}{d x} - 2 x y - x^{2} \frac{d y}{d x} + y + x \frac{d y}{d x}

= y^{2} + 2 x y \frac{d y}{d x} - 2 x y - x^{2} \frac{d y}{d x} + y + x \frac{d y}{d x}

\int \frac{x ^{3}}{( x ^{2} - 256 ) ^{\frac{3}{2}}} d x

s l o p e (0, - 10), (6, 10)

t a y l or \frac{1}{x}, at 1

\int e^{iπ z} d z

d er i v a t i v e f (t) = t - \frac{1}{t}