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Beliebt Rechnen >

(\partial)/(\partial x)(9xsin(4x^2y))

Lösung

\frac{\partial}{\partial x} (9 x sin (4 x^{2} y))

Lösung

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

Schritte zur Lösung

\frac{\partial}{\partial x} (9 x sin (4 x^{2} y))

Behandle

y

als Konstante

Entferne die Konstante:

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

= 9 \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)

= 9 (\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

= 9 (1 \cdot sin (4 x^{2} y) + cos (4 x^{2} y) \cdot 8 y xx)

Vereinfache

9 (1 \cdot sin (4 x^{2} y) + cos (4 x^{2} y) \cdot 8 y xx) : 9 (sin (4 x^{2} y) + 8 x^{2} y cos (4 x^{2} y))

= 9 (sin (4 x^{2} y) + 8 x^{2} y cos (4 x^{2} y))

Beliebte Beispiele

derivative f(t)=t^2

d er i v a t i v e f (t) = t^{2}

derivative of ((4x^2+8x+2)/(sqrt(x)))

\frac{d}{d x} (\frac{( 4 x ^{2} + 8 x + 2 )}{x})

derivative of (-3/(sqrt(x)))

\frac{d}{d x} (\frac{- 3}{x})

integral of sqrt(x)(sqrt(x)+1)^2

\int x (x + 1)^{2} d x

(dy)/(dx)=x^3(x-xy)

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