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Beliebt Rechnen >

(\partial)/(\partial x)(x^3-5x^2+y^3-8y)

Lösung

\frac{\partial}{\partial x} (x^{3} - 5 x^{2} + y^{3} - 8 y)

Lösung

3 x^{2} - 10 x

Schritte zur Lösung

\frac{\partial}{\partial x} (x^{3} - 5 x^{2} + y^{3} - 8 y)

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial x} (x^{3}) - \frac{\partial}{\partial x} (5 x^{2}) + \frac{\partial}{\partial x} (y^{3}) - \frac{\partial}{\partial x} (8 y)

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

\frac{\partial}{\partial x} (5 x^{2}) = 10 x

\frac{\partial}{\partial x} (y^{3}) = 0

\frac{\partial}{\partial x} (8 y) = 0

= 3 x^{2} - 10 x + 0 - 0

Vereinfache

= 3 x^{2} - 10 x

Beliebte Beispiele

integral of (1-5/y+x)

\int (1 - \frac{5}{y} + x) d y

derivative y=(4e)^x

d er i v a t i v e y = (4 e)^{x}

derivative of (1-5x^2/(\sqrt[3]{3+2x)})

\frac{d}{d x} (\frac{1 - 5 x ^{2}}{3 3 + 2 x})

d/(dy)(xln(xy))

\frac{d}{d y} (x ln (x y))

derivative f(x)=(2x+7)^2

d er i v a t i v e f (x) = (2 x + 7)^{2}