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Beliebt Rechnen >

(\partial)/(\partial x)(4cos(xy^2))

Lösung

\frac{\partial}{\partial x} (4 cos (x y^{2}))

Lösung

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

Schritte zur Lösung

\frac{\partial}{\partial x} (4 cos (x y^{2}))

Behandle

y

als Konstante

Entferne die Konstante:

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

= 4 \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}

= 4 (- sin (x y^{2}) y^{2})

Vereinfache

= - 4 y^{2} sin (x y^{2})

Beliebte Beispiele

integral of (x^3-1/(2x)+1)

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

integral of-sin(-x)

\int - sin (- x) d x

(\partial)/(\partial x)(sqrt(x^3+x))

\frac{\partial}{\partial x} (x^{3} + x)

integral from b to 1 of 3ln(x)

\int_{b}^{1} 3 ln (x) d x

integral of 5x 3/2

\int 5 x \frac{3}{2} d x