derivative x^2ln(2x)

Lösung

ableitung von

x^{2} 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

\int \frac{( x + 3 ) ^{2}}{2 x} d x

\int (3 x^{3} + 4 x^{2} - 2 x^{- 1} + 13) d x

l a pl a ce t r an s f or m t^{2} cos (5 t)

d er i v a t i v e \frac{sin ( x )}{2 + cos ( x )}

t a y l or sin (5 x), x = 0