(\partial)/(\partial x)(4x(x^2+y^2)-4a^2x)

Lösung

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

4 (3 x^{2} + y^{2}) - 4 a^{2}

Schritte zur Lösung

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

Behandle

a, y

als Konstante

Wende die Summen-/Differenzregel an:

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

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

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

\frac{\partial}{\partial x} (4 a^{2} x) = 4 a^{2}

= 4 (3 x^{2} + y^{2}) - 4 a^{2}

d er i v a t i v e \frac{a}{x}

in v erse l a pl a ce \frac{s}{( s - 1 )}

y (1 + x^{2}) y^{^{'}} - x (6 + y^{2}) = 0

d er i v a t i v e y = 5 x^{4} e^{x} + e^{x} x^{5}

x \to 1 lim (- 6 + 2 x^{2})