derivative of 3x^4ln(x)

Lösung

\frac{d}{d x} (3 x^{4} ln (x))

3 (4 x^{3} ln (x) + x^{3})

Schritte zur Lösung

\frac{d}{d x} (3 x^{4} ln (x))

Entferne die Konstante:

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

= 3 \frac{d}{d x} (x^{4} ln (x))

Wende die Produktregel an:

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

f = x^{4}, g = ln (x)

= 3 (\frac{d}{d x} (x^{4}) ln (x) + \frac{d}{d x} (ln (x)) x^{4})

\frac{d}{d x} (x^{4}) = 4 x^{3}

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

= 3 (4 x^{3} ln (x) + \frac{1}{x} x^{4})

\frac{1}{x} x^{4} = x^{3}

= 3 (4 x^{3} ln (x) + x^{3})

\int 8 e^{2 x} + 6 x d x

\frac{\partial}{\partial x} (9 x arctan (\frac{x}{y}))

y = e^{- x} sin (π) x

x \to 1 lim ({3 f (x) - 2 h (x)})

x \to 0 lim (\frac{cos ( 3 x )}{x + 3})