derivative of 3/(sqrt(7x^4-5x^2+1))

解答

\frac{d}{d x} (\frac{3}{7 x ^{4} - 5 x ^{2} + 1})

- \frac{3 x ( 14 x ^{2} - 5 )}{( 7 x ^{4} - 5 x ^{2} + 1 ) ^{\frac{3}{2}}}

求解步骤

\frac{d}{d x} (\frac{3}{7 x ^{4} - 5 x ^{2} + 1})

将常数提出:

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

= 3 \frac{d}{d x} (\frac{1}{7 x ^{4} - 5 x ^{2} + 1})

使用指数法则:

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

= 3 \frac{d}{d x} ((7 x^{4} - 5 x^{2} + 1)^{- \frac{1}{2}})

使用连锁律:

- \frac{1}{2 ( 7 x ^{4} - 5 x ^{2} + 1 ) ^{\frac{3}{2}}} \frac{d}{d x} (7 x^{4} - 5 x^{2} + 1)

= - \frac{1}{2 ( 7 x ^{4} - 5 x ^{2} + 1 ) ^{\frac{3}{2}}} \frac{d}{d x} (7 x^{4} - 5 x^{2} + 1)

\frac{d}{d x} (7 x^{4} - 5 x^{2} + 1) = 28 x^{3} - 10 x

= 3 (- \frac{1}{2 ( 7 x ^{4} - 5 x ^{2} + 1 ) ^{\frac{3}{2}}} (28 x^{3} - 10 x))

化简

3 (- \frac{1}{2 ( 7 x ^{4} - 5 x ^{2} + 1 ) ^{\frac{3}{2}}} (28 x^{3} - 10 x)) : - \frac{3 x ( 14 x ^{2} - 5 )}{( 7 x ^{4} - 5 x ^{2} + 1 ) ^{\frac{3}{2}}}

= - \frac{3 x ( 14 x ^{2} - 5 )}{( 7 x ^{4} - 5 x ^{2} + 1 ) ^{\frac{3}{2}}}

x \to 0.1 lim (\frac{e ^{x} - 1}{x})

d er i v a t i v e f (x) = (6 x - x^{2})^{10}

\frac{d}{d x} (sin^{5} (3 x))

y^{^{'}} = 4 - 9 x^{2} - 6 x^{5}

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