(\partial)/(\partial x)(1/2 (x^2+10y^2))

Lösung

\frac{\partial}{\partial x} (\frac{1}{2} (x^{2} + 10 y^{2}))

x

Schritte zur Lösung

\frac{\partial}{\partial x} (\frac{1}{2} (x^{2} + 10 y^{2}))

Behandle

y

als Konstante

Entferne die Konstante:

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

= \frac{1}{2} \frac{\partial}{\partial x} (x^{2} + 10 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} (10 y^{2}))

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

\frac{\partial}{\partial x} (10 y^{2}) = 0

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

Vereinfache

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

= x

f (x) = x - cos (x)

\int_{0}^{6} 2. 3^{t} sin (\frac{t}{2}) d t

\int \frac{( 2 x + 4 )}{x ^{2} + 4 x + 5} d x

\int \frac{x ^{2} + 2 x + 3}{x ^{3} + 3 x ^{2} + 9 x + 1} d x

\int \frac{1}{2 x ^{2} + x} d x