derivative of x^2*ln(2x)

Lösung

\frac{d}{d x} (x^{2} \cdot ln (2 x))

2 x ln (2 x) + x

Schritte zur Lösung

\frac{d}{d x} (x^{2} ln (2 x))

Wende die Produktregel an:

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

f = x^{2}, g = ln (2 x)

= \frac{d}{d x} (x^{2}) ln (2 x) + \frac{d}{d x} (ln (2 x)) x^{2}

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

\frac{d}{d x} (ln (2 x)) = \frac{1}{x}

= 2 x ln (2 x) + \frac{1}{x} x^{2}

\frac{1}{x} x^{2} = x

= 2 x ln (2 x) + x

in v erse l a pl a ce \frac{s}{s ^{2} + 25}

121 y^{^{''}} - 16 y = 0

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

n = 1 \sum \infty \frac{1}{n ^{2} + 3 n + 2}

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