derivative of 30x^4y^7-24x^{12}y^3

Lösung

\frac{d}{d x} (30 x^{4} y^{7} - 24 x^{12} y^{3})

30 (4 x^{3} y^{7} + 7 y^{6} \frac{d y}{d x} x^{4}) - 24 (12 x^{11} y^{3} + 3 y^{2} \frac{d y}{d x} x^{12})

Schritte zur Lösung

\frac{d}{d x} (30 x^{4} y^{7} - 24 x^{12} y^{3})

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (30 x^{4} y^{7}) - \frac{d}{d x} (24 x^{12} y^{3})

\frac{d}{d x} (30 x^{4} y^{7}) = 30 (4 x^{3} y^{7} + 7 y^{6} \frac{d y}{d x} x^{4})

\frac{d}{d x} (24 x^{12} y^{3}) = 24 (12 x^{11} y^{3} + 3 y^{2} \frac{d y}{d x} x^{12})

= 30 (4 x^{3} y^{7} + 7 y^{6} \frac{d y}{d x} x^{4}) - 24 (12 x^{11} y^{3} + 3 y^{2} \frac{d y}{d x} x^{12})

\frac{d}{d x} (- e^{x^{2}})

\frac{\partial}{\partial y} (x + ln (y))

\int_{1}^{e^{5}} x^{4} ln (x) d x

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

\int_{- 1}^{2} (3 x + 1) d x