(\partial)/(\partial x)(ln(5x^2+4y^2+7))

Lösung

\frac{\partial}{\partial x} (ln (5 x^{2} + 4 y^{2} + 7))

\frac{10 x}{5 x ^{2} + 4 y ^{2} + 7}

Schritte zur Lösung

\frac{\partial}{\partial x} (ln (5 x^{2} + 4 y^{2} + 7))

Behandle

y

als Konstante

Wende die Kettenregel an:

\frac{1}{5 x ^{2} + 4 y ^{2} + 7} \frac{\partial}{\partial x} (5 x^{2} + 4 y^{2} + 7)

= \frac{1}{5 x ^{2} + 4 y ^{2} + 7} \frac{\partial}{\partial x} (5 x^{2} + 4 y^{2} + 7)

\frac{\partial}{\partial x} (5 x^{2} + 4 y^{2} + 7) = 10 x

= \frac{1}{5 x ^{2} + 4 y ^{2} + 7} \cdot 10 x

Vereinfache

\frac{1}{5 x ^{2} + 4 y ^{2} + 7} \cdot 10 x : \frac{10 x}{5 x ^{2} + 4 y ^{2} + 7}

= \frac{10 x}{5 x ^{2} + 4 y ^{2} + 7}

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

l a pl a ce t r an s f or m z

\int \frac{12}{3 x + x x} d x

(3 + 3 x^{2}) \frac{d y}{d x} + 2 x y = 2 x y^{4}

d er i v a t i v e f (x) = ln (2)