derivative of 3xy^2+2ycos(x)

Lösung

\frac{d}{d x} (3 x y^{2} + 2 y cos (x))

3 (y^{2} + 2 x y \frac{d y}{d x}) + 2 (cos (x) \frac{d y}{d x} - sin (x) y)

Schritte zur Lösung

\frac{d}{d x} (3 x y^{2} + 2 y cos (x))

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (3 x y^{2}) + \frac{d}{d x} (2 y cos (x))

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

\frac{d}{d x} (2 y cos (x)) = 2 (cos (x) \frac{d y}{d x} - sin (x) y)

= 3 (y^{2} + 2 x y \frac{d y}{d x}) + 2 (cos (x) \frac{d y}{d x} - sin (x) y)

\int x^{2} (x^{3} - 1)^{4} d x

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

x y + y^{^{'}} = 80 x

\int_{3}^{4} (4 + \frac{24}{x ^{2}}) d x

\frac{d y}{d x} + 7 x y = 0