(\partial)/(\partial z)(x-z-arctan(yz))

Lösung

\frac{\partial}{\partial z} (x - z - arctan (yz))

- \frac{y}{z ^{2} y ^{2} + 1} - 1

Schritte zur Lösung

\frac{\partial}{\partial z} (x - z - arctan (yz))

Behandle

x, y

als Konstanten

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial z} (x) - \frac{\partial}{\partial z} (z) - \frac{\partial}{\partial z} (arctan (yz))

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

\frac{\partial}{\partial z} (z) = 1

\frac{\partial}{\partial z} (arctan (yz)) = \frac{y}{y ^{2} z ^{2} + 1}

= 0 - 1 - \frac{y}{y ^{2} z ^{2} + 1}

Vereinfache

= - \frac{y}{z ^{2} y ^{2} + 1} - 1

\int 6 x sec (x) tan (x) d x

\frac{d}{d x} (ln (x^{2} + 10))

\frac{d}{d t} (10000 (12 + t) e^{- 0.05 t})

\int \frac{5}{( 3 x - 1 )} d x

\frac{d}{d x} (e^{60 x + 50 x^{2}})