(\partial)/(\partial x)(sqrt(2x^2-5y^2))

Lösung

\frac{\partial}{\partial x} (2 x^{2} - 5 y^{2})

\frac{2 x}{2 x ^{2} - 5 y ^{2}}

Schritte zur Lösung

\frac{\partial}{\partial x} (2 x^{2} - 5 y^{2})

Behandle

y

als Konstante

Wende die Kettenregel an:

\frac{1}{2 2 x ^{2} - 5 y ^{2}} \frac{\partial}{\partial x} (2 x^{2} - 5 y^{2})

= \frac{1}{2 2 x ^{2} - 5 y ^{2}} \frac{\partial}{\partial x} (2 x^{2} - 5 y^{2})

\frac{\partial}{\partial x} (2 x^{2} - 5 y^{2}) = 4 x

= \frac{1}{2 2 x ^{2} - 5 y ^{2}} \cdot 4 x

Vereinfache

\frac{1}{2 2 x ^{2} - 5 y ^{2}} \cdot 4 x : \frac{2 x}{2 x ^{2} - 5 y ^{2}}

= \frac{2 x}{2 x ^{2} - 5 y ^{2}}

\int_{- 2}^{6} 4 x - x^{2} + 12 d x

y^{^{''}} + 5 y^{^{'}} = e^{- t}, y (0) = 0, y^{^{'}} (0) = 1

x \to 4 lim (f (x))

f (x) = - \frac{1}{x}

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