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

解答

导数

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

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

求解步骤

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

使用连锁律:

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

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

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

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

化简

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

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

t a y l or ln (1 + x), 0

y^{^{'}} + 3 y = e^{- 3 t}

\int_{0}^{1} 3 x^{3} d x

\int_{0}^{2} - x^{2} + 4 d x

\frac{d}{d y} (x e^{- y})