(\partial)/(\partial x)(sqrt(3x^2+7y^2))

Lösung

\frac{\partial}{\partial x} (3 x^{2} + 7 y^{2})

\frac{3 x}{3 x ^{2} + 7 y ^{2}}

Schritte zur Lösung

\frac{\partial}{\partial x} (3 x^{2} + 7 y^{2})

Behandle

y

als Konstante

Wende die Kettenregel an:

\frac{1}{2 3 x ^{2} + 7 y ^{2}} \frac{\partial}{\partial x} (3 x^{2} + 7 y^{2})

= \frac{1}{2 3 x ^{2} + 7 y ^{2}} \frac{\partial}{\partial x} (3 x^{2} + 7 y^{2})

\frac{\partial}{\partial x} (3 x^{2} + 7 y^{2}) = 6 x

= \frac{1}{2 3 x ^{2} + 7 y ^{2}} \cdot 6 x

Vereinfache

\frac{1}{2 3 x ^{2} + 7 y ^{2}} \cdot 6 x : \frac{3 x}{3 x ^{2} + 7 y ^{2}}

= \frac{3 x}{3 x ^{2} + 7 y ^{2}}

s l o p e (2.3) (4.7)

\int - ln ∣ 1 - x ∣ d x

\int_{0}^{H} z^{2} (1 - z)^{2} d z

(x^{2} + y) + (x + e^{y}) y^{^{'}} = 0

\frac{d y}{d x} = \frac{cos ( 10 x )}{e ^{10 y}}