derivative (x+1)(7sqrt(x)+2)

解答

导数

(x + 1) (7 x + 2)

\frac{21 x + 7}{2 x} + 2

求解步骤

\frac{d}{d x} ((x + 1) (7 x + 2))

使用微分乘法定则:

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

f = x + 1, g = 7 x + 2

= \frac{d}{d x} (x + 1) (7 x + 2) + \frac{d}{d x} (7 x + 2) (x + 1)

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

\frac{d}{d x} (7 x + 2) = \frac{7}{2 x}

= 1 \cdot (7 x + 2) + \frac{7}{2 x} (x + 1)

化简

1 \cdot (7 x + 2) + \frac{7}{2 x} (x + 1) : \frac{21 x + 7}{2 x} + 2

= \frac{21 x + 7}{2 x} + 2

\frac{\partial}{\partial x} (\frac{x}{y ^{2}} + x y + 8)

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

t a y l or z (z + 1) e^{z}

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

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