(\partial)/(\partial x)(5x^4+2xy^2+1)

Lösung

\frac{\partial}{\partial x} (5 x^{4} + 2 x y^{2} + 1)

20 x^{3} + 2 y^{2}

Schritte zur Lösung

\frac{\partial}{\partial x} (5 x^{4} + 2 x y^{2} + 1)

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial x} (5 x^{4}) + \frac{\partial}{\partial x} (2 x y^{2}) + \frac{\partial}{\partial x} (1)

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

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

\frac{\partial}{\partial x} (1) = 0

= 20 x^{3} + 2 y^{2} + 0

Vereinfache

= 20 x^{3} + 2 y^{2}

\frac{d}{d y} ((\frac{1}{y ^{2}} - \frac{5}{y ^{4}}) (y + 7 y^{3}))

a re a x^{2} - 3 x, 2 x + 6

\frac{\partial}{\partial z} (x^{2} y - 3 x z + 5 y + 7 z)

\frac{d}{d x} (20 sin (x))

\int - \frac{10}{x ^{11}} d x