derivative of 2xy^3

Lösung

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

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

Schritte zur Lösung

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

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= 2 \frac{d}{d x} (x y^{3})

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = y^{3}

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

\frac{d x}{d x} = 1

\frac{d}{d x} (y^{3}) = 3 y^{2} \frac{d y}{d x}

= 2 (1 \cdot y^{3} + 3 y^{2} \frac{d y}{d x} x)

Vereinfache

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

\frac{\partial}{\partial y} (e^{s i n (x + y)})

t an g e n t f (x) = 1 + 4 csc (x), at x = - \frac{π}{3}

n = 1 \sum \infty \frac{2}{3 n + 10}

\int_{1}^{2} 4 x 4 x^{2} + 4 d x

\int (3 x^{4} - 5 x^{2} + 6 x) d x