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Beliebt Rechnen >

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

Lösung

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

Lösung

4 x

Schritte zur Lösung

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

Behandle

y, z

als Konstanten

Wende die Summen-/Differenzregel an:

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

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

\frac{\partial}{\partial x} (2 x^{2}) = 4 x

\frac{\partial}{\partial x} (3 y^{2}) = 0

\frac{\partial}{\partial x} (5 z^{2}) = 0

= 4 x + 0 + 0

Vereinfache

= 4 x

Beliebte Beispiele

steigung y=(((x+2))/((x-2)^2)),\at x=3

s l o p e y = (\frac{( x + 2 )}{( x - 2 ) ^{2}}), at x = 3

derivative of (x^2-3/(e^x))

\frac{d}{d x} (\frac{x ^{2} - 3}{e ^{x}})

derivative f(x)=(x^2+5)^9

d er i v a t i v e f (x) = (x^{2} + 5)^{9}

integral of t^3e^{t^2}

\int t^{3} e^{t^{2}} d t

implicit (dy)/(dx),15x=15y+5y^3+3y^5

im pl i c i t \frac{d y}{d x}, 15 x = 15 y + 5 y^{3} + 3 y^{5}