(\partial)/(\partial x)(2cos(xy^2))

Lösung

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

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

Schritte zur Lösung

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

Behandle

y

als Konstante

Entferne die Konstante:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

d er i v a t i v e \frac{( 4 x ^{2} + 8 x + 6 )}{x}

x \to 0 lim (∣ x - 4 ∣)

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

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

y^{^{''}} + a^{2} y = 0