(\partial)/(\partial x)(-(5x^3+5xy^2))

Lösung

\frac{\partial}{\partial x} (- (5 x^{3} + 5 x y^{2}))

- 15 x^{2} - 5 y^{2}

Schritte zur Lösung

\frac{\partial}{\partial x} (- (5 x^{3} + 5 x y^{2}))

Vereinfache

- (5 x^{3} + 5 x y^{2}) : - 5 x^{3} - 5 x y^{2}

= \frac{\partial}{\partial x} (- 5 x^{3} - 5 x y^{2})

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

= - \frac{\partial}{\partial x} (5 x^{3}) - \frac{\partial}{\partial x} (5 x y^{2})

\frac{\partial}{\partial x} (5 x^{3}) = 15 x^{2}

\frac{\partial}{\partial x} (5 x y^{2}) = 5 y^{2}

= - 15 x^{2} - 5 y^{2}

\frac{\partial}{\partial h} (x^{2} h)

ma c l a u r in \frac{1}{x + 2}

\int \frac{x ^{2} - 2}{x ^{2} + x} d x

(x + 2) \frac{d y}{d x} + y = ln (x), y (1) = 20

a re a x, x^{2}, 0, 1