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

Lösung

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

8 x^{3} y^{3}

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

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

\frac{\partial}{\partial x} (2 x^{4} y^{3}) = 8 y^{3} x^{3}

\frac{\partial}{\partial x} (y) = 0

= 8 y^{3} x^{3} + 0

Vereinfache

= 8 x^{3} y^{3}

\int \frac{5}{x + 6} d x

x \to + 0 lim (x ln (\frac{1}{x}))

s im pl i f y (sin (x)) (sec (x))

\int_{- 1}^{1} \frac{1}{2} (1 - x^{4}) d x

\int \frac{x ^{3} + 5 x + 1}{x ^{2} + 5} d x