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Beliebt Rechnen >

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

Lösung

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

Lösung

4 x^{3} sin (x y^{3}) + cos (x y^{3}) y^{3} x^{4}

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Produktregel an:

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

f = x^{4}, g = sin (x y^{3})

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

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

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

= 4 x^{3} sin (x y^{3}) + cos (x y^{3}) y^{3} x^{4}

Beliebte Beispiele

integral of ((arctan(5x)))/(1+25x^2)

derivative of-x^5

integral of (1+x^3)^5x^2

d/(dy)(xsqrt(y))

x^2y^'+4xy=(sin(3x))/(x^2)