(\partial)/(\partial x)(sqrt(4x^2+4y+2z^2))

Lösung

\frac{\partial}{\partial x} (4 x^{2} + 4 y + 2 z^{2})

\frac{4 x}{4 x ^{2} + 4 y + 2 z ^{2}}

Schritte zur Lösung

\frac{\partial}{\partial x} (4 x^{2} + 4 y + 2 z^{2})

Behandle

y, z

als Konstanten

Wende die Kettenregel an:

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

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

\frac{\partial}{\partial x} (4 x^{2} + 4 y + 2 z^{2}) = 8 x

= \frac{1}{2 4 x ^{2} + 4 y + 2 z ^{2}} \cdot 8 x

Vereinfache

\frac{1}{2 4 x ^{2} + 4 y + 2 z ^{2}} \cdot 8 x : \frac{4 x}{4 x ^{2} + 4 y + 2 z ^{2}}

= \frac{4 x}{4 x ^{2} + 4 y + 2 z ^{2}}

\frac{d}{d x} (\frac{x ^{2} + 2 x}{( x + 1 ) ^{2}})

d er i v a t i v e y = a^{4} + cos^{4} (x)

\int [5 sin^{2} (3 x) + tan (2 x)] d x

\frac{d}{d x} (4 x + 8 + \frac{14400}{x})

\int 2 x + 4 e^{x} d x