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Beliebt Rechnen >

(\partial)/(\partial x)(2x^3y+cos(x^4))

Lösung

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

Lösung

6 y x^{2} - sin (x^{4}) \cdot 4 x^{3}

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{\partial}{\partial x} (2 x^{3} y) = 6 y x^{2}

\frac{\partial}{\partial x} (cos (x^{4})) = - sin (x^{4}) \cdot 4 x^{3}

= 6 y x^{2} - sin (x^{4}) \cdot 4 x^{3}

Beliebte Beispiele

integral of x^2sqrt(15+x^3)

\int x^{2} 15 + x^{3} d x

derivative of (a+bx^2/(x^2))

\frac{d}{d x} (\frac{a + b x ^{2}}{x ^{2}})

derivative of ((x^4}{12}+\frac{(x^3))/3)

\frac{d}{d x} (\frac{( x ^{4} )}{12} + \frac{( x ^{3} )}{3})

limit as x approaches 0 of tan^x(5x)

x \to 0 lim (tan^{x} (5 x))

(\partial)/(\partial x)(x+2y)

\frac{\partial}{\partial x} (x + 2 y)