(\partial)/(\partial x)(3y^2cos(5x))

Lösung

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

- 15 y^{2} sin (5 x)

Schritte zur Lösung

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

Behandle

y

als Konstante

Entferne die Konstante:

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

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

Wende die Kettenregel an:

- sin (5 x) \frac{\partial}{\partial x} (5 x)

= - sin (5 x) \frac{\partial}{\partial x} (5 x)

\frac{\partial}{\partial x} (5 x) = 5

= 3 y^{2} (- sin (5 x) \cdot 5)

Vereinfache

= - 15 y^{2} sin (5 x)

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

\int \frac{1}{( ln ( x ) ) ^{2}} d x

\frac{\partial}{\partial y} (2 arctan (\frac{y}{x}))

t an g e n t f (x) = 2 + 3 x - 5 x^{2}, at x = 1

h \to 1 lim (4 h^{2} + x + 3)