derivative of 7/(x+4)

解答

\frac{d}{d x} (\frac{7}{x + 4})

- \frac{7}{( x + 4 ) ^{2}}

求解步骤

\frac{d}{d x} (\frac{7}{x + 4})

将常数提出:

(a \cdot f)^{'} = a \cdot f^{'}

= 7 \frac{d}{d x} (\frac{1}{x + 4})

使用指数法则:

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

= 7 \frac{d}{d x} ((x + 4)^{- 1})

使用连锁律:

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

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

\frac{d}{d x} (x + 4) = 1

= 7 (- \frac{1}{( x + 4 ) ^{2}} \cdot 1)

化简

7 (- \frac{1}{( x + 4 ) ^{2}} \cdot 1) : - \frac{7}{( x + 4 ) ^{2}}

= - \frac{7}{( x + 4 ) ^{2}}

d x - e^{3 x} d y = 0

\frac{\partial}{\partial x} (x^{6 y})

\int_{b}^{d} \frac{1}{r} d r

t an g e n t f (x) = 7 x^{3} + 5 x, at x = 7

\frac{d}{d x} (3 e^{x} (5 x^{5} - 2))