(\partial)/(\partial x)(4ax^4+7b(x,t)t^3)

Lösung

\frac{\partial}{\partial x} (4 a x^{4} + 7 b (x, t) t^{3})

16 a x^{3} + 7 t^{3} \frac{\partial}{\partial x} (b (x, t))

Schritte zur Lösung

\frac{\partial}{\partial x} (4 a x^{4} + 7 b (x, t) t^{3})

Behandle

a, t

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial x} (4 a x^{4}) + \frac{\partial}{\partial x} (7 b (x, t) t^{3})

\frac{\partial}{\partial x} (4 a x^{4}) = 16 a x^{3}

\frac{\partial}{\partial x} (7 b (x, t) t^{3}) = 7 t^{3} \frac{\partial}{\partial x} (b (x, t))

= 16 a x^{3} + 7 t^{3} \frac{\partial}{\partial x} (b (x, t))

d er i v a t i v e y = \frac{4 + x f ( x )}{x}

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

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

d er i v a t i v e arctan (\frac{x - 1}{x + 1})

d er i v a t i v e ln (sin (x))