derivative xln(2x)

解答

导数

x ln (2 x)

ln (2 x) + 1

求解步骤

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

使用微分乘法定则:

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

f = x, g = ln (2 x)

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

\frac{d x}{d x} = 1

\frac{d}{d x} (ln (2 x)) = \frac{1}{x}

= 1 \cdot ln (2 x) + \frac{1}{x} x

化简

1 \cdot ln (2 x) + \frac{1}{x} x : ln (2 x) + 1

= ln (2 x) + 1

\int cos^{4} (x) d x

\frac{d}{d t} (a_{2} t cos (2 t) + a_{2} t sin (2 t))

\int 1

\frac{d}{d x} ((x + 1)^{\frac{2}{3}} - x^{\frac{2}{3}} + 1)

\int \frac{1 - u ^{2}}{u + u ^{3}} d u