(\partial)/(\partial y)(4x^3y^3-3x^2sin(x^3)y)

Lösung

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

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

Schritte zur Lösung

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

Behandle

x

als Konstante

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{\partial}{\partial y} (4 x^{3} y^{3}) = 12 x^{3} y^{2}

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

= 12 x^{3} y^{2} - 3 x^{2} sin (x^{3})

\frac{d}{d x} (\frac{( x ^{2} - 1 ) ^{3}}{( 2 x + 1 ) ^{5}})

\int_{- 2}^{4} (x^{2} - 2 x - 8) d x

x \to \infty lim (\frac{sin ( 17 x )}{x})

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

\frac{d}{d x} (\frac{x cos ( x )}{1 + e ^{x}})