(\partial)/(\partial x)(4x^4y^8+9x^6y^7)

Lösung

\frac{\partial}{\partial x} (4 x^{4} y^{8} + 9 x^{6} y^{7})

16 y^{8} x^{3} + 54 y^{7} x^{5}

Schritte zur Lösung

\frac{\partial}{\partial x} (4 x^{4} y^{8} + 9 x^{6} y^{7})

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial x} (4 x^{4} y^{8}) + \frac{\partial}{\partial x} (9 x^{6} y^{7})

\frac{\partial}{\partial x} (4 x^{4} y^{8}) = 16 y^{8} x^{3}

\frac{\partial}{\partial x} (9 x^{6} y^{7}) = 54 y^{7} x^{5}

= 16 y^{8} x^{3} + 54 y^{7} x^{5}

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

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