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

Lösung

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

\frac{14 x}{x ^{2} + y ^{2}}

Schritte zur Lösung

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

Behandle

y

als Konstante

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

7 \cdot \frac{1}{x ^{2} + y ^{2}} \cdot 2 x : \frac{14 x}{x ^{2} + y ^{2}}

= \frac{14 x}{x ^{2} + y ^{2}}

x^{^{''}} - 5 x^{^{'}} + 6 x = e^{t}

\int 7 tan (x) d x

\frac{d}{d x} (- \frac{x ^{3}}{3})

\int \frac{8 x ^{3}}{3} d x

\frac{d}{d x} (3 x^{2} cos (x^{3}))