d/(d{y)}(({x}^2+{y}^2+{z}^2)^{-1/2}+ln({x}{y}{z}))

Lösung

\frac{d}{d y} ((x^{2} + y^{2} + z^{2})^{- \frac{1}{2}} + ln (x y z))

- \frac{y}{( x ^{2} + y ^{2} + z ^{2} ) ^{\frac{3}{2}}} + \frac{1}{y}

Schritte zur Lösung

\frac{d}{d y} ((x^{2} + y^{2} + z^{2})^{- \frac{1}{2}} + ln (x y z))

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d y} ((x^{2} + y^{2} + z^{2})^{- \frac{1}{2}}) + \frac{d}{d y} (ln (x y z))

\frac{d}{d y} ((x^{2} + y^{2} + z^{2})^{- \frac{1}{2}}) = - \frac{y}{( x ^{2} + y ^{2} + z ^{2} ) ^{\frac{3}{2}}}

\frac{d}{d y} (ln (x y z)) = \frac{1}{y}

= - \frac{y}{( x ^{2} + y ^{2} + z ^{2} ) ^{\frac{3}{2}}} + \frac{1}{y}

\int tan^{7} (x) sec^{4} (x) d x

x \to - 2 lim (5 (3 x^{2} - 24 x + 3))

x \to 0 lim (\frac{- 9}{1 - 9 x})

\frac{\partial}{\partial x} (y \cdot cos (x))

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