derivative of 3x^5ln(x)

Lösung

\frac{d}{d x} (3 x^{5} ln (x))

3 (5 x^{4} ln (x) + x^{4})

Schritte zur Lösung

\frac{d}{d x} (3 x^{5} ln (x))

Entferne die Konstante:

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

= 3 \frac{d}{d x} (x^{5} ln (x))

Wende die Produktregel an:

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

f = x^{5}, g = ln (x)

= 3 (\frac{d}{d x} (x^{5}) ln (x) + \frac{d}{d x} (ln (x)) x^{5})

\frac{d}{d x} (x^{5}) = 5 x^{4}

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

= 3 (5 x^{4} ln (x) + \frac{1}{x} x^{5})

\frac{1}{x} x^{5} = x^{4}

= 3 (5 x^{4} ln (x) + x^{4})

t an g e n t f (x) = \frac{4 x ^{2}}{x + 2}

\frac{d}{d x} (\frac{d y}{d x}) + 4 y = 2 sin (2 x)

\int \frac{6}{9 + 6 x} d x

h \to 0 lim (2 + h)

\frac{d}{d x} (- 6 x^{3})