derivative of 6x^2+5x^3y^4-10y^5

Lösung

\frac{d}{d x} (6 x^{2} + 5 x^{3} y^{4} - 10 y^{5})

12 x + 5 (3 x^{2} y^{4} + 4 y^{3} \frac{d y}{d x} x^{3}) - 50 y^{4} \frac{d y}{d x}

Schritte zur Lösung

\frac{d}{d x} (6 x^{2} + 5 x^{3} y^{4} - 10 y^{5})

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (6 x^{2}) + \frac{d}{d x} (5 x^{3} y^{4}) - \frac{d}{d x} (10 y^{5})

\frac{d}{d x} (6 x^{2}) = 12 x

\frac{d}{d x} (5 x^{3} y^{4}) = 5 (3 x^{2} y^{4} + 4 y^{3} \frac{d y}{d x} x^{3})

\frac{d}{d x} (10 y^{5}) = 50 y^{4} \frac{d y}{d x}

= 12 x + 5 (3 x^{2} y^{4} + 4 y^{3} \frac{d y}{d x} x^{3}) - 50 y^{4} \frac{d y}{d x}

\int tan (3 x) sin (3 x) d x

\int (5 x + 4)^{6} d x

f (x) = (2 x + 1)^{6}

t (\frac{d y}{d t}) = t^{3} + 13 t^{3} y

\frac{d}{d x} (9 x e^{- x})