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Beliebt Rechnen >

(\partial)/(\partial x)(-sin(x^2y)x^2)

Lösung

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

Lösung

- 2 x^{3} y cos (x^{2} y) - 2 x sin (x^{2} y)

Schritte zur Lösung

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

Behandle

y

als Konstante

Entferne die Konstante:

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

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

Wende die Produktregel an:

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

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

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

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

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

= - (cos (x^{2} y) \cdot 2 y x x^{2} + 2 x sin (x^{2} y))

Vereinfache

- (cos (x^{2} y) \cdot 2 y x x^{2} + 2 x sin (x^{2} y)) : - 2 x^{3} y cos (x^{2} y) - 2 x sin (x^{2} y)

= - 2 x^{3} y cos (x^{2} y) - 2 x sin (x^{2} y)

Beliebte Beispiele

integral of t*1/(e^t)

\int t \cdot \frac{1}{e ^{t}} d t

integral of (-2sec(x)tan(x)-3sec^2(x))

\int (- 2 sec (x) tan (x) - 3 sec^{2} (x)) d x

5t*(dy)/(dt)+3y=sqrt(t)

5 t \cdot \frac{d y}{d t} + 3 y = t

(dx)/(dt)=((2t^2+x^2))/(tx)

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

y^{''}-2y^'+5y=e^xsin(x)

y^{^{''}} - 2 y^{^{'}} + 5 y = e^{x} sin (x)