derivative of 3x^5ln(x)

解答

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

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

求解步骤

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

将常数提出:

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

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

使用微分乘法定则:

(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})