(\partial)/(\partial x)(sqrt(15-2x^2-y^2))

Lösung

\frac{\partial}{\partial x} (15 - 2 x^{2} - y^{2})

- \frac{2 x}{15 - 2 x ^{2} - y ^{2}}

Schritte zur Lösung

\frac{\partial}{\partial x} (15 - 2 x^{2} - y^{2})

Behandle

y

als Konstante

Wende die Kettenregel an:

\frac{1}{2 15 - 2 x ^{2} - y ^{2}} \frac{\partial}{\partial x} (15 - 2 x^{2} - y^{2})

= \frac{1}{2 15 - 2 x ^{2} - y ^{2}} \frac{\partial}{\partial x} (15 - 2 x^{2} - y^{2})

\frac{\partial}{\partial x} (15 - 2 x^{2} - y^{2}) = - 4 x

= \frac{1}{2 15 - 2 x ^{2} - y ^{2}} (- 4 x)

Vereinfache

\frac{1}{2 15 - 2 x ^{2} - y ^{2}} (- 4 x) : - \frac{2 x}{15 - 2 x ^{2} - y ^{2}}

= - \frac{2 x}{15 - 2 x ^{2} - y ^{2}}

d er i v a t i v e (3 + x^{4})^{\frac{4}{5}}

x \to 0 + lim (\frac{10}{x ^{2}})

d er i v a t i v e f (x) = \frac{x}{x + 2}

\frac{d y}{d t} = 9 t^{2}

x \to - 2 lim (3 x^{2} - 3 x - 8)