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

Lösung

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

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

Schritte zur Lösung

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

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^{3}))

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

\frac{\partial}{\partial x} (cos (x^{3})) = - sin (x^{3}) \cdot 3 x^{2}

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

\frac{\partial}{\partial y} (\frac{100}{5 x ^{2} + y ^{2}})

in v erse l a pl a ce \frac{s}{s ^{2} + 4 s}

\int \frac{x ^{3} + 4}{x ^{2}} d x

\frac{\partial}{\partial x} (5 x^{5} y^{8} + 8 x^{6} y^{7})

\int_{0}^{\infty} \frac{x}{1 + x ^{4}} d x