(\partial)/(\partial x)(xln(x))

Lösung

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

ln (x) + 1

Schritte zur Lösung

\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)

= \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}

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

Vereinfache

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

= ln (x) + 1

n \to \infty lim (n^{4} + 2 n^{3} - (n^{2} + n))

d er i v a t i v e \frac{8 x}{e ^{x}}

\int_{0}^{5} 5 x - 1 d x

\int_{0}^{1} (9 x^{e} + 2 e^{x}) d x

\frac{d y}{d x} = 2 x y^{2} + 3 x^{2} y^{2}