derivative y=(7ln(x))/(3x+4)

解答

导数

y = \frac{7 ln ( x )}{3 x + 4}

\frac{7 ( 3 x + 4 - 3 x ln ( x ) )}{x ( 3 x + 4 ) ^{2}}

求解步骤

\frac{d}{d x} (\frac{7 ln ( x )}{3 x + 4})

将常数提出:

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

= 7 \frac{d}{d x} (\frac{ln ( x )}{3 x + 4})

使用微分除法定则:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= 7 \cdot \frac{\frac{d}{d x} ( ln ( x ) ) ( 3 x + 4 ) - \frac{d}{d x} ( 3 x + 4 ) ln ( x )}{( 3 x + 4 ) ^{2}}

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

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

= 7 \cdot \frac{\frac{1}{x} ( 3 x + 4 ) - 3 ln ( x )}{( 3 x + 4 ) ^{2}}

化简

7 \cdot \frac{\frac{1}{x} ( 3 x + 4 ) - 3 ln ( x )}{( 3 x + 4 ) ^{2}} : \frac{7 ( 3 x + 4 - 3 x ln ( x ) )}{x ( 3 x + 4 ) ^{2}}

= \frac{7 ( 3 x + 4 - 3 x ln ( x ) )}{x ( 3 x + 4 ) ^{2}}

x \to \frac{1}{3} lim (3 x^{3} + 2 x^{2})

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\frac{\partial}{\partial x} (2 x \cdot y - \frac{1}{2} x^{2})

f (t) = 6 sin (t)

\int_{- 1}^{3} \frac{x}{x ^{2} + 4} d x