(\partial)/(\partial y)(y^x-ln(x^3y+6x))

Lösung

\frac{\partial}{\partial y} (y^{x} - ln (x^{3} y + 6 x))

x y^{x - 1} - \frac{x ^{2}}{x ^{2} y + 6}

Schritte zur Lösung

\frac{\partial}{\partial y} (y^{x} - ln (x^{3} y + 6 x))

Behandle

x

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial y} (y^{x}) - \frac{\partial}{\partial y} (ln (x^{3} y + 6 x))

\frac{\partial}{\partial y} (y^{x}) = x y^{x - 1}

\frac{\partial}{\partial y} (ln (x^{3} y + 6 x)) = \frac{x ^{2}}{x ^{2} y + 6}

= x y^{x - 1} - \frac{x ^{2}}{x ^{2} y + 6}

x \to - 4 + lim (\frac{- 6 x}{x + 4})

\frac{\partial}{\partial x} (arctan (\frac{1}{x}))

\int e^{- s t} t sin (t) d t

d er i v a t i v e f (x) = \frac{2}{( 1 - x ) ^{2}}

x \to 1 + lim (\frac{∣ 1 - x ∣}{1 - x})