(\partial)/(\partial x)(1/2 (x^2+6y^2))

Lösung

\frac{\partial}{\partial x} (\frac{1}{2} (x^{2} + 6 y^{2}))

x

Schritte zur Lösung

\frac{\partial}{\partial x} (\frac{1}{2} (x^{2} + 6 y^{2}))

Behandle

y

als Konstante

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{1}{2} \frac{\partial}{\partial x} (x^{2} + 6 y^{2})

Wende die Summen-/Differenzregel an:

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

= \frac{1}{2} (\frac{\partial}{\partial x} (x^{2}) + \frac{\partial}{\partial x} (6 y^{2}))

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

\frac{\partial}{\partial x} (6 y^{2}) = 0

= \frac{1}{2} (2 x + 0)

Vereinfache

\frac{1}{2} (2 x + 0) : x

= x

t an g e n t f (x) = x (x^{2} - 4 x + 5)^{4}, at x = 2

\int \frac{e ^{- s t}}{s} d t

\int ln (6 x + 1) d x

\frac{d}{d x} (sin (e^{x} - 1))

t an g e n t 4 x^{3} - 4 x^{2} + 3