derivative (4.5x-4)/((3x-4)^{1/2)}

解答

导数

\frac{4.5 x - 4}{( 3 x - 4 ) ^{\frac{1}{2}}}

\frac{4.5 ( 3 x - 4 ) ^{\frac{1}{2}} - \frac{1.5 ( 4.5 x - 4 )}{( 3 x - 4 ) ^{\frac{1}{2}}}}{3 x - 4}

求解步骤

\frac{d}{d x} (\frac{4.5 x - 4}{( 3 x - 4 ) ^{\frac{1}{2}}})

使用微分除法定则:

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

= \frac{\frac{d}{d x} ( 4.5 x - 4 ) ( 3 x - 4 ) ^{\frac{1}{2}} - \frac{d}{d x} ( ( 3 x - 4 ) ^{\frac{1}{2}} ) ( 4.5 x - 4 )}{( ( 3 x - 4 ) ^{\frac{1}{2}} ) ^{2}}

\frac{d}{d x} (4.5 x - 4) = 4.5

\frac{d}{d x} ((3 x - 4)^{\frac{1}{2}}) = \frac{3}{2 ( 3 x - 4 ) ^{\frac{1}{2}}}

= \frac{4.5 ( 3 x - 4 ) ^{\frac{1}{2}} - \frac{3}{2 ( 3 x - 4 ) ^{\frac{1}{2}}} ( 4.5 x - 4 )}{( ( 3 x - 4 ) ^{\frac{1}{2}} ) ^{2}}

化简

\frac{4.5 ( 3 x - 4 ) ^{\frac{1}{2}} - \frac{3}{2 ( 3 x - 4 ) ^{\frac{1}{2}}} ( 4.5 x - 4 )}{( ( 3 x - 4 ) ^{\frac{1}{2}} ) ^{2}} : \frac{4.5 ( 3 x - 4 ) ^{\frac{1}{2}} - \frac{1.5 ( 4.5 x - 4 )}{( 3 x - 4 ) ^{\frac{1}{2}}}}{3 x - 4}

= \frac{4.5 ( 3 x - 4 ) ^{\frac{1}{2}} - \frac{1.5 ( 4.5 x - 4 )}{( 3 x - 4 ) ^{\frac{1}{2}}}}{3 x - 4}

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

\frac{d}{d x} (\frac{9}{x ^{3}} + \frac{1}{x})

\int_{0}^{1} (x^{3})^{2} d x

im pl i c i t \frac{d y}{d x}, e^{x} y = 5

\frac{d}{d x} (4 x^{3})