(\partial)/(\partial x)(4sin(x^3y^2))

Lösung

\frac{\partial}{\partial x} (4 sin (x^{3} y^{2}))

12 x^{2} y^{2} cos (x^{3} y^{2})

Schritte zur Lösung

\frac{\partial}{\partial x} (4 sin (x^{3} y^{2}))

Behandle

y

als Konstante

Entferne die Konstante:

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

= 4 \frac{\partial}{\partial x} (sin (x^{3} y^{2}))

Wende die Kettenregel an:

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

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

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

= 4 cos (x^{3} y^{2}) \cdot 3 y^{2} x^{2}

Vereinfache

= 12 x^{2} y^{2} cos (x^{3} y^{2})

d er i v a t i v e \frac{( 3 u ^{2} )}{( u ^{2} + u ) ^{3}}

\int_{1}^{2} \frac{3}{x ^{2}} - 1 d x

x \to 0 lim (\frac{x}{x})

s l o p e (3, 1), (5, - 4)

\int \frac{1}{9 x ^{2} - 36 x + 37} d x