(\partial)/(\partial x)(x^3+e^{y^2})

Lösung

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

3 x^{2}

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

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

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

\frac{\partial}{\partial x} (e^{y^{2}}) = 0

= 3 x^{2} + 0

Vereinfache

= 3 x^{2}

y^{^{'}} + y = sin (x)

n = 1 \sum \infty n

d er i v a t i v e f (x) = ln (4 x)

y^{^{''}} + y^{^{'}} + 5 y = 0, y (0) = 0, y^{^{'}} (0) = 0

h \to 0 lim (\frac{2 ^{h} - 1}{h})