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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Behandle

y

als Konstante

Entferne die Konstante:

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

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

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{2}, g = cos (x)

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

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

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

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

Vereinfache

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

Beliebte Beispiele

(\partial)/(\partial x)(ln(1+xy))

\frac{\partial}{\partial x} (ln (1 + x y))

derivative f(x)=(2x+3)/(3x+2)

d er i v a t i v e f (x) = \frac{2 x + 3}{3 x + 2}

(\partial)/(\partial x)((e^{x-y})goog)

\frac{\partial}{\partial x} ((e^{x - y}) g oo g)

tangent f(x)=1-2cos(x)

t an g e n t f (x) = 1 - 2 cos (x)

derivative of ((x-5/(x+5))^4)

\frac{d}{d x} ((\frac{x - 5}{x + 5})^{4})