(\partial)/(\partial x)(ln(x^2+3y^2+8))

Lösung

\frac{\partial}{\partial x} (ln (x^{2} + 3 y^{2} + 8))

\frac{2 x}{x ^{2} + 3 y ^{2} + 8}

Schritte zur Lösung

\frac{\partial}{\partial x} (ln (x^{2} + 3 y^{2} + 8))

Behandle

y

als Konstante

Wende die Kettenregel an:

\frac{1}{x ^{2} + 3 y ^{2} + 8} \frac{\partial}{\partial x} (x^{2} + 3 y^{2} + 8)

= \frac{1}{x ^{2} + 3 y ^{2} + 8} \frac{\partial}{\partial x} (x^{2} + 3 y^{2} + 8)

\frac{\partial}{\partial x} (x^{2} + 3 y^{2} + 8) = 2 x

= \frac{1}{x ^{2} + 3 y ^{2} + 8} \cdot 2 x

Vereinfache

\frac{1}{x ^{2} + 3 y ^{2} + 8} \cdot 2 x : \frac{2 x}{x ^{2} + 3 y ^{2} + 8}

= \frac{2 x}{x ^{2} + 3 y ^{2} + 8}

\int \frac{1}{( x - 2 ) ( x - 4 ) ( x + 1 )} d x

d er i v a t i v e x + 2

a re a x = - y^{2} + 4 y, [1, 4]

x \to 0 lim (sin^{2} (\frac{π}{x}))

\frac{\partial}{\partial x} ((9 x + 2 y)^{10})