derivative of x^4ln(9x)

解

\frac{d}{d x} (x^{4} ln (9 x))

4 x^{3} ln (9 x) + x^{3}

解答ステップ

\frac{d}{d x} (x^{4} ln (9 x))

積の法則を適用:

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

f = x^{4}, g = ln (9 x)

= \frac{d}{d x} (x^{4}) ln (9 x) + \frac{d}{d x} (ln (9 x)) x^{4}

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

\frac{d}{d x} (ln (9 x)) = \frac{1}{x}

= 4 x^{3} ln (9 x) + \frac{1}{x} x^{4}

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

= 4 x^{3} ln (9 x) + x^{3}