derivative of x^2ln(x^3)

Lösung

\frac{d}{d x} (x^{2} ln (x^{3}))

6 x ln (x) + 3 x

Schritte zur Lösung

\frac{d}{d x} (x^{2} ln (x^{3}))

Wende die Produktregel an:

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

f = x^{2}, g = ln (x^{3})

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

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

\frac{d}{d x} (ln (x^{3})) = \frac{3}{x}

= 2 x ln (x^{3}) + \frac{3}{x} x^{2}

Vereinfache

2 x ln (x^{3}) + \frac{3}{x} x^{2} : 6 x ln (x) + 3 x

= 6 x ln (x) + 3 x

f (x) = ln (1 - x^{2})

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

\frac{d}{d x} (e^{6})

k = 0 \sum \infty \frac{k}{3 ^{k}}

s im pl i f y 1 \cdot sin (x) + x \cdot cos (x)