derivative of 3xy^2

Lösung

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

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

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Produktregel an:

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

f = x, g = y^{2}

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

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

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

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

Vereinfache

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

\frac{d}{d x} (\frac{sin ( y )}{sin ( x )})

d er i v a t i v e y (θ) = \frac{π}{8} sin (θ)

\int \frac{1}{b ^{2} 25 + b ^{2}} d b

\frac{d}{d x} (2 - 4 cos (x))

y^{^{'}} = \frac{x y}{1 - x ^{2}}