derivative of ax^2+by(x^2+c)

Lösung

\frac{d}{d x} (a x^{2} + b y (x) (x)^{2} + c)

2 a x + b (x^{2} \frac{d}{d x} (y (x)) + 2 x y (x))

Schritte zur Lösung

\frac{d}{d x} (a x^{2} + b y (x) (x)^{2} + c)

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (a x^{2}) + \frac{d}{d x} (b y (x) x^{2}) + \frac{d c}{d x}

\frac{d}{d x} (a x^{2}) = 2 a x

\frac{d}{d x} (b y (x) x^{2}) = b (\frac{d}{d x} (y (x)) x^{2} + 2 x y (x))

\frac{d c}{d x} = 0

= 2 a x + b (\frac{d}{d x} (y (x)) x^{2} + 2 x y (x)) + 0

Vereinfache

= 2 a x + b (x^{2} \frac{d}{d x} (y (x)) + 2 x y (x))

\int_{0}^{y} \int_{0}^{x} (x^{2} + y^{2})^{\frac{3}{2}} d y d x

a re a 3 x, \frac{3}{4} x, 70 - x^{2}

y^{^{'}} = \frac{( y + y ^{2} )}{x ^{2}}

\int_{0}^{3} ∣ 3 x - 1 ∣ d x

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