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Beliebt Rechnen >

(\partial)/(\partial x)(3xsin(4x^2y))

Lösung

\frac{\partial}{\partial x} (3 x sin (4 x^{2} y))

Lösung

3 (sin (4 x^{2} y) + 8 x^{2} y cos (4 x^{2} y))

Schritte zur Lösung

\frac{\partial}{\partial x} (3 x sin (4 x^{2} y))

Behandle

y

als Konstante

Entferne die Konstante:

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

= 3 \frac{\partial}{\partial x} (x sin (4 x^{2} y))

Wende die Produktregel an:

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

f = x, g = sin (4 x^{2} y)

= 3 (\frac{\partial}{\partial x} (x) sin (4 x^{2} y) + \frac{\partial}{\partial x} (sin (4 x^{2} y)) x)

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

\frac{\partial}{\partial x} (sin (4 x^{2} y)) = cos (4 x^{2} y) \cdot 8 y x

= 3 (1 \cdot sin (4 x^{2} y) + cos (4 x^{2} y) \cdot 8 y xx)

Vereinfache

3 (1 \cdot sin (4 x^{2} y) + cos (4 x^{2} y) \cdot 8 y xx) : 3 (sin (4 x^{2} y) + 8 x^{2} y cos (4 x^{2} y))

= 3 (sin (4 x^{2} y) + 8 x^{2} y cos (4 x^{2} y))

Beliebte Beispiele

fläche y=3(x+1),y=4(x+1),x=3

a re a y = 3 (x + 1), y = 4 (x + 1), x = 3

integral from 0 to (3pi)/2 of 2|sin(x)|

\int_{0}^{\frac{3 π}{2}} 2 ∣ sin (x) ∣ d x

integral of e^{y/3}

\int e^{\frac{y}{3}} d y

derivative (x^2-4x+2)/(x+3)

d er i v a t i v e \frac{x ^{2} - 4 x + 2}{x + 3}

limit as x approaches 1 of sqrt(x^2-1)

x \to 1 lim (x^{2} - 1)