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Beliebt Rechnen >

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

Lösung

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

Lösung

3 x^{5} y^{2} cos (x y^{3})

Schritte zur Lösung

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

Behandle

x

als Konstante

Entferne die Konstante:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

x^{4} cos (x y^{3}) \cdot 3 x y^{2} : 3 x^{5} y^{2} cos (x y^{3})

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

Beliebte Beispiele

limit as x approaches infinity of (log_{2}(x))/(sqrt(x))

x \to \infty lim (\frac{lo g _{2} ( x )}{x})

f (x) = 2 x^{4}

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

\int \frac{x ^{2} - 1}{x ^{2}} d x

integral of x^2e^{-18x}

\int x^{2} e^{- 18 x} d x

(2x^4+y^4)dy-x^3ydx=0

(2 x^{4} + y^{4}) d y - x^{3} y d x = 0