derivative y= 1/((3x+8)^2)

解答

导数

y = \frac{1}{( 3 x + 8 ) ^{2}}

- \frac{6}{( 3 x + 8 ) ^{3}}

求解步骤

\frac{d}{d x} (\frac{1}{( 3 x + 8 ) ^{2}})

使用指数法则:

\frac{1}{a} = a^{- 1}

= \frac{d}{d x} ((3 x + 8)^{- 2})

使用连锁律:

- \frac{2}{( 3 x + 8 ) ^{3}} \frac{d}{d x} (3 x + 8)

= - \frac{2}{( 3 x + 8 ) ^{3}} \frac{d}{d x} (3 x + 8)

\frac{d}{d x} (3 x + 8) = 3

= - \frac{2}{( 3 x + 8 ) ^{3}} \cdot 3

化简

- \frac{2}{( 3 x + 8 ) ^{3}} \cdot 3 : - \frac{6}{( 3 x + 8 ) ^{3}}

= - \frac{6}{( 3 x + 8 ) ^{3}}

x \to - 3 lim (5 x)

d er i v a t i v e - 2 9 s^{2} + 1

x \to 2 - lim (f (x))

\frac{d}{d x} ((x^{2} 7^{x})^{9})

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