(\partial)/(\partial x)(x^5+x^2y+x+1)

Lösung

\frac{\partial}{\partial x} (x^{5} + x^{2} y + x + 1)

5 x^{4} + 2 x y + 1

Schritte zur Lösung

\frac{\partial}{\partial x} (x^{5} + x^{2} y + x + 1)

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial x} (x^{5}) + \frac{\partial}{\partial x} (x^{2} y) + \frac{\partial}{\partial x} (x) + \frac{\partial}{\partial x} (1)

\frac{\partial}{\partial x} (x^{5}) = 5 x^{4}

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

\frac{\partial}{\partial x} (x) = 1

\frac{\partial}{\partial x} (1) = 0

= 5 x^{4} + 2 y x + 1 + 0

Vereinfache

= 5 x^{4} + 2 x y + 1

\int \frac{13}{( t ^{2} + 1 ) ^{\frac{3}{2}}} d t

(x^{2} + 1) \frac{d y}{d x} = x (y^{2} + 1)

a re a x^{2} - 6 x - 7, - x^{2} + 2 x + 3

\int 5 sin^{5} (x) cos (x) d x

x \to - 1 + lim (8 x^{2} + 5 m)