(\partial)/(\partial x)(8x^5y^3-9x^4y^6)

Lösung

\frac{\partial}{\partial x} (8 x^{5} y^{3} - 9 x^{4} y^{6})

40 y^{3} x^{4} - 36 y^{6} x^{3}

Schritte zur Lösung

\frac{\partial}{\partial x} (8 x^{5} y^{3} - 9 x^{4} y^{6})

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial x} (8 x^{5} y^{3}) - \frac{\partial}{\partial x} (9 x^{4} y^{6})

\frac{\partial}{\partial x} (8 x^{5} y^{3}) = 40 y^{3} x^{4}

\frac{\partial}{\partial x} (9 x^{4} y^{6}) = 36 y^{6} x^{3}

= 40 y^{3} x^{4} - 36 y^{6} x^{3}

\frac{d}{d x} (\frac{4 x ^{3} + 1}{x ^{2} - x + 3})

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

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

\frac{d}{d x} (x + 7)

im pl i c i t \frac{d y}{d x}, x^{2} + 5 x + 9 x y - y^{2} = 4