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Beliebt Rechnen >

(\partial)/(\partial x)(ln(x+y^3)-z)

Lösung

\frac{\partial}{\partial x} (ln (x + y^{3}) - z)

Lösung

\frac{1}{x + y ^{3}}

Schritte zur Lösung

\frac{\partial}{\partial x} (ln (x + y^{3}) - z)

Behandle

y, z

als Konstanten

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial x} (ln (x + y^{3})) - \frac{\partial}{\partial x} (z)

\frac{\partial}{\partial x} (ln (x + y^{3})) = \frac{1}{x + y ^{3}}

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

= \frac{1}{x + y ^{3}} - 0

Vereinfache

= \frac{1}{x + y ^{3}}

Beliebte Beispiele

integral of (8x^7)/((x^8+1)^2)

\int \frac{8 x ^{7}}{( x ^{8} + 1 ) ^{2}} d x

derivative of (dx/x)

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

derivative (1+3t)^2

d er i v a t i v e (1 + 3 t)^{2}

d/(dt)(tsin(t)+cos(t))

\frac{d}{d t} (t sin (t) + cos (t))

integral of ((1-x))/(x^2)

\int \frac{( 1 - x )}{x ^{2}} d x