derivative of cxln(x)

解答

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

c (ln (x) + 1)

求解步骤

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

将常数提出:

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

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

使用微分乘法定则:

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

f = x, g = ln (x)

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

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

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

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

化简

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

= c (ln (x) + 1)

(- x^{2} sin (x) + 2 π x sin (x) - 2 π cos (x) + 2 π)^{^{'}}

\frac{d}{d x} (\frac{1 + cos ( x )}{2})

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