(\partial)/(\partial x)(30x^5y^4-20x^4y^3)

Lösung

\frac{\partial}{\partial x} (30 x^{5} y^{4} - 20 x^{4} y^{3})

150 y^{4} x^{4} - 80 y^{3} x^{3}

Schritte zur Lösung

\frac{\partial}{\partial x} (30 x^{5} y^{4} - 20 x^{4} y^{3})

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial x} (30 x^{5} y^{4}) - \frac{\partial}{\partial x} (20 x^{4} y^{3})

\frac{\partial}{\partial x} (30 x^{5} y^{4}) = 150 y^{4} x^{4}

\frac{\partial}{\partial x} (20 x^{4} y^{3}) = 80 y^{3} x^{3}

= 150 y^{4} x^{4} - 80 y^{3} x^{3}

x \to - 2 lim (\frac{1}{x ^{2}})

t an g e n t x^{2} + y^{2} = 169, (12, - 5)

\frac{d}{d x} ((4 x - 13) ln ((2 x - 7) (x - 3)))

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