derivative of 2x^2y^2

Lösung

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

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

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Produktregel an:

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

f = x^{2}, g = y^{2}

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

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

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

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

d er i v a t i v e z + 3 (\frac{1}{z ^{2}})

\frac{d y}{d x} + y tan (x) = 2 x cos (x)

\frac{\partial}{\partial z} (x y + yz + x z)

\int \frac{1}{3} x^{3} d x

\int_{0}^{1} \frac{6}{1 - x ^{2}} d x