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

Lösung

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

\frac{16 x}{8 x ^{2} + 3 y ^{2} + 3}

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Kettenregel an:

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

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

\frac{\partial}{\partial x} (8 x^{2} + 3 y^{2} + 3) = 16 x

= \frac{1}{8 x ^{2} + 3 y ^{2} + 3} \cdot 16 x

Vereinfache

\frac{1}{8 x ^{2} + 3 y ^{2} + 3} \cdot 16 x : \frac{16 x}{8 x ^{2} + 3 y ^{2} + 3}

= \frac{16 x}{8 x ^{2} + 3 y ^{2} + 3}

\int \frac{10 x ^{4} - 9 x ^{2}}{2 x ^{5} - 3 x ^{3} + 14} d x

\frac{\partial}{\partial x} (\frac{5 y}{x ^{3}})

y^{^{''}} - 9 y^{^{'}} + 18 y = 5 sin (4 t), y (0) = 5, y^{^{'}} (0) = 2

t a y l or x e^{- 3 x}

y^{^{'}} - y = 3 t e^{2 t}