(\partial)/(\partial x)(xln(y)+y^2z+z^2)

Lösung

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

ln (y)

Schritte zur Lösung

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

Behandle

y, z

als Konstanten

Wende die Summen-/Differenzregel an:

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

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

\frac{\partial}{\partial x} (x ln (y)) = ln (y)

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

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

= ln (y) + 0 + 0

Vereinfache

= ln (y)

d er i v a t i v e f (x) = 6 x - 3

\frac{d x}{d y} = \frac{2 y + sec ^{2} ( y )}{2 x}

\int_{0}^{0.5} 250 x d x

\int \frac{x}{1 + 2 x} d x

\frac{d}{d x} (- (x + 3) (x - 9)^{2})