(\partial)/(\partial x)(4xln(x)y)

Lösung

\frac{\partial}{\partial x} (4 x ln (x) y)

4 y (ln (x) + 1)

Schritte zur Lösung

\frac{\partial}{\partial x} (4 x ln (x) y)

Behandle

y

als Konstante

Entferne die Konstante:

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

= 4 y \frac{\partial}{\partial x} (x ln (x))

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = ln (x)

= 4 y (\frac{\partial}{\partial x} (x) ln (x) + \frac{\partial}{\partial x} (ln (x)) x)

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

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

= 4 y (1 \cdot ln (x) + \frac{1}{x} x)

Vereinfache

4 y (1 \cdot ln (x) + \frac{1}{x} x) : 4 y (ln (x) + 1)

= 4 y (ln (x) + 1)

\int (2 x + y)^{8} d x

x \to 0 + lim ((x)^{- x^{2}})

in v erse l a pl a ce t e^{2 t}

y^{^{''}} + 5 y^{^{'}} + 4 y = sin (3 x)

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