derivative of 5/((x-6^2))

解答

\frac{d}{d x} (\frac{5}{( x - 6 ) ^{2}})

- \frac{10}{( x - 6 ) ^{3}}

求解步骤

\frac{d}{d x} (\frac{5}{( x - 6 ) ^{2}})

将常数提出:

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

= 5 \frac{d}{d x} (\frac{1}{( x - 6 ) ^{2}})

使用指数法则:

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

= 5 \frac{d}{d x} ((x - 6)^{- 2})

使用连锁律:

- \frac{2}{( x - 6 ) ^{3}} \frac{d}{d x} (x - 6)

= - \frac{2}{( x - 6 ) ^{3}} \frac{d}{d x} (x - 6)

\frac{d}{d x} (x - 6) = 1

= 5 (- \frac{2}{( x - 6 ) ^{3}} \cdot 1)

化简

5 (- \frac{2}{( x - 6 ) ^{3}} \cdot 1) : - \frac{10}{( x - 6 ) ^{3}}

= - \frac{10}{( x - 6 ) ^{3}}

\int_{\frac{1}{5}}^{3} 8 x ln (5 x) d x

d er i v a t i v e ln (e)

\int x^{\frac{3}{4}} d x

y^{^{''}} + 289 y = sec (17 x)

d er i v a t i v e f (x) = 2 x^{5} - 3 e^{6 x}