(\partial)/(\partial x)(6y^2-4y^3-3x^2+6xy)

Lösung

\frac{\partial}{\partial x} (6 y^{2} - 4 y^{3} - 3 x^{2} + 6 x y)

6 y - 6 x

Schritte zur Lösung

\frac{\partial}{\partial x} (6 y^{2} - 4 y^{3} - 3 x^{2} + 6 x y)

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial x} (6 y^{2}) - \frac{\partial}{\partial x} (4 y^{3}) - \frac{\partial}{\partial x} (3 x^{2}) + \frac{\partial}{\partial x} (6 x y)

\frac{\partial}{\partial x} (6 y^{2}) = 0

\frac{\partial}{\partial x} (4 y^{3}) = 0

\frac{\partial}{\partial x} (3 x^{2}) = 6 x

\frac{\partial}{\partial x} (6 x y) = 6 y

= 0 - 0 - 6 x + 6 y

Vereinfache

= 6 y - 6 x

t an g e n t f (x) = \frac{6}{5 x + 2}, at x = - 1

d er i v a t i v e f (x) = arctan (x)

\int \frac{1}{sin ( θ )} d θ

\int \frac{1}{3 x - 3} d x

\int_{4}^{6} \frac{x}{x ^{2} + 6 x + 13} d x