(\partial)/(\partial x)(sqrt(4-x^2-4Y(x)^2))

Lösung

\frac{\partial}{\partial x} (4 - x^{2} - 4 Y (x) (x)^{2})

- \frac{x ( 2 ( x \frac{\partial}{\partial x} ( Y ( x ) ) + 2 Y ( x ) ) + 1 )}{- x ^{2} - 4 x ^{2} Y ( x ) + 4}

Schritte zur Lösung

\frac{\partial}{\partial x} (4 - x^{2} - 4 Y (x) (x)^{2})

Wende die Kettenregel an:

\frac{1}{2 4 - x ^{2} - 4 Y ( x ) x ^{2}} \frac{\partial}{\partial x} (4 - x^{2} - 4 Y (x) x^{2})

= \frac{1}{2 4 - x ^{2} - 4 Y ( x ) x ^{2}} \frac{\partial}{\partial x} (4 - x^{2} - 4 Y (x) x^{2})

\frac{\partial}{\partial x} (4 - x^{2} - 4 Y (x) x^{2}) = - 2 x - 4 (x^{2} \frac{\partial}{\partial x} (Y (x)) + 2 x Y (x))

= \frac{1}{2 4 - x ^{2} - 4 Y ( x ) x ^{2}} (- 2 x - 4 (x^{2} \frac{\partial}{\partial x} (Y (x)) + 2 x Y (x)))

Vereinfache

\frac{1}{2 4 - x ^{2} - 4 Y ( x ) x ^{2}} (- 2 x - 4 (x^{2} \frac{\partial}{\partial x} (Y (x)) + 2 x Y (x))) : - \frac{x ( 2 ( x \frac{\partial}{\partial x} ( Y ( x ) ) + 2 Y ( x ) ) + 1 )}{- x ^{2} - 4 x ^{2} Y ( x ) + 4}

= - \frac{x ( 2 ( x \frac{\partial}{\partial x} ( Y ( x ) ) + 2 Y ( x ) ) + 1 )}{- x ^{2} - 4 x ^{2} Y ( x ) + 4}

\frac{d}{d x} (- x^{3} + 5 x^{2} - 6 x)

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

d er i v a t i v e y = \frac{4}{5 - 3 ( x )}

x \to 4 lim (\frac{x}{x - 4})

\int_{0}^{4} x (4 - x) d x