(\partial)/(\partial x)(4xsin(6x^2y))

Lösung

\frac{\partial}{\partial x} (4 x sin (6 x^{2} y))

4 (sin (6 x^{2} y) + 12 x^{2} y cos (6 x^{2} y))

Schritte zur Lösung

\frac{\partial}{\partial x} (4 x sin (6 x^{2} y))

Behandle

y

als Konstante

Entferne die Konstante:

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

= 4 \frac{\partial}{\partial x} (x sin (6 x^{2} y))

Wende die Produktregel an:

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

f = x, g = sin (6 x^{2} y)

= 4 (\frac{\partial}{\partial x} (x) sin (6 x^{2} y) + \frac{\partial}{\partial x} (sin (6 x^{2} y)) x)

\frac{\partial}{\partial x} (x) = 1

\frac{\partial}{\partial x} (sin (6 x^{2} y)) = cos (6 x^{2} y) \cdot 12 y x

= 4 (1 \cdot sin (6 x^{2} y) + cos (6 x^{2} y) \cdot 12 y xx)

Vereinfache

4 (1 \cdot sin (6 x^{2} y) + cos (6 x^{2} y) \cdot 12 y xx) : 4 (sin (6 x^{2} y) + 12 x^{2} y cos (6 x^{2} y))

= 4 (sin (6 x^{2} y) + 12 x^{2} y cos (6 x^{2} y))

\frac{d y}{d x} = x y - x

y^{^{''}} + 2 y^{^{'}} - 3 y = 0

x \to a lim (\frac{1}{x})

\frac{d y}{d x} = 5 y^{2}

\int \frac{2 x}{x ^{2} - 9} d x