(\partial)/(\partial y)(3x^2y+5xy^3)

Lösung

\frac{\partial}{\partial y} (3 x^{2} y + 5 x y^{3})

3 x^{2} + 15 x y^{2}

Schritte zur Lösung

\frac{\partial}{\partial y} (3 x^{2} y + 5 x y^{3})

Behandle

x

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial y} (3 x^{2} y) + \frac{\partial}{\partial y} (5 x y^{3})

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

\frac{\partial}{\partial y} (5 x y^{3}) = 15 x y^{2}

= 3 x^{2} + 15 x y^{2}

d er i v a t i v e \frac{( 3 - x )}{4 x}

\int cos^{4} (3 - x) sin (3 - x) d x

a re a y = x, y = 1 - x^{2}, - 1, 2

t an g e n t - \frac{39}{( 8 x + 5 ) ^{2}}, at x = 2

\int_{0}^{4} \frac{12}{x ^{2} + 5 x + 6} d x