derivative f(x)=(6x)/(3+x)

解答

导数

f (x) = \frac{6 x}{3 + x}

\frac{18}{( 3 + x ) ^{2}}

求解步骤

\frac{d}{d x} (\frac{6 x}{3 + x})

将常数提出:

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

= 6 \frac{d}{d x} (\frac{x}{3 + x})

使用微分除法定则:

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

= 6 \cdot \frac{\frac{d x}{d x} ( 3 + x ) - \frac{d}{d x} ( 3 + x ) x}{( 3 + x ) ^{2}}

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

\frac{d}{d x} (3 + x) = 1

= 6 \cdot \frac{1 \cdot ( 3 + x ) - 1 \cdot x}{( 3 + x ) ^{2}}

化简

6 \cdot \frac{1 \cdot ( 3 + x ) - 1 \cdot x}{( 3 + x ) ^{2}} : \frac{18}{( 3 + x ) ^{2}}

= \frac{18}{( 3 + x ) ^{2}}

\frac{d}{d x} (144 - x^{2})

d er i v a t i v e 1 + x

x y^{^{'}} - y = \frac{2}{3} x ln (x)

d er i v a t i v e x^{2.4} + e^{2.4}

x \to 4 - lim (\frac{15}{x - 4})