derivative of 1/(2x+5)

解答

\frac{d}{d x} (\frac{1}{2 x + 5})

- \frac{2}{( 2 x + 5 ) ^{2}}

求解步骤

\frac{d}{d x} (\frac{1}{2 x + 5})

使用指数法则:

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

= \frac{d}{d x} ((2 x + 5)^{- 1})

使用连锁律:

- \frac{1}{( 2 x + 5 ) ^{2}} \frac{d}{d x} (2 x + 5)

= - \frac{1}{( 2 x + 5 ) ^{2}} \frac{d}{d x} (2 x + 5)

\frac{d}{d x} (2 x + 5) = 2

= - \frac{1}{( 2 x + 5 ) ^{2}} \cdot 2

化简

- \frac{1}{( 2 x + 5 ) ^{2}} \cdot 2 : - \frac{2}{( 2 x + 5 ) ^{2}}

= - \frac{2}{( 2 x + 5 ) ^{2}}

\int \frac{cos ^{2} ( x )}{1 - sin ( x )} d x

x \to 2 lim (9 x)

t an g e n t 5 x + 6, at x = 2

t an g e n t y = e^{3 x}, at x = \frac{1}{3} ln (3)

y (x + 1) + \frac{d y}{d x} = 0