derivative of 4xy^2-x^2y^2-xy^3

Lösung

\frac{d}{d x} (4 x y^{2} - x^{2} y^{2} - x y^{3})

4 y^{2} + 8 x y \frac{d y}{d x} - 2 x y^{2} - 2 x^{2} y \frac{d y}{d x} - y^{3} - 3 x y^{2} \frac{d y}{d x}

Schritte zur Lösung

\frac{d}{d x} (4 x y^{2} - x^{2} y^{2} - x y^{3})

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (4 x y^{2}) - \frac{d}{d x} (x^{2} y^{2}) - \frac{d}{d x} (x y^{3})

\frac{d}{d x} (4 x y^{2}) = 4 (y^{2} + 2 x y \frac{d y}{d x})

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

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

= 4 (y^{2} + 2 x y \frac{d y}{d x}) - (2 x y^{2} + 2 y \frac{d y}{d x} x^{2}) - (y^{3} + 3 x y^{2} \frac{d y}{d x})

Vereinfache

4 (y^{2} + 2 x y \frac{d y}{d x}) - (2 x y^{2} + 2 y \frac{d y}{d x} x^{2}) - (y^{3} + 3 x y^{2} \frac{d y}{d x}) : 4 y^{2} + 8 x y \frac{d y}{d x} - 2 x y^{2} - 2 x^{2} y \frac{d y}{d x} - y^{3} - 3 x y^{2} \frac{d y}{d x}

= 4 y^{2} + 8 x y \frac{d y}{d x} - 2 x y^{2} - 2 x^{2} y \frac{d y}{d x} - y^{3} - 3 x y^{2} \frac{d y}{d x}

\int - \frac{1}{2} x^{\frac{1}{2}} d x

t an g e n t f (x) = - 3 x^{2} + 3 x + 1, at x = 1

d er i v a t i v e y = \frac{2}{1 - 9 x ^{2}}

\int_{0}^{\frac{π}{2}} x cos (\frac{x}{3}) d x

d er i v a t i v e \frac{2 ln ( x )}{x}