derivative 4x^{5/4}+8x^{3/2}+3x

解答

导数

4 x^{\frac{5}{4}} + 8 x^{\frac{3}{2}} + 3 x

5 x^{\frac{1}{4}} + 12 x^{\frac{1}{2}} + 3

求解步骤

\frac{d}{d x} (4 x^{\frac{5}{4}} + 8 x^{\frac{3}{2}} + 3 x)

使用微分加减法定则:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (4 x^{\frac{5}{4}}) + \frac{d}{d x} (8 x^{\frac{3}{2}}) + \frac{d}{d x} (3 x)

\frac{d}{d x} (4 x^{\frac{5}{4}}) = 5 x^{\frac{1}{4}}

\frac{d}{d x} (8 x^{\frac{3}{2}}) = 12 x^{\frac{1}{2}}

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

= 5 x^{\frac{1}{4}} + 12 x^{\frac{1}{2}} + 3

y^{^{'}} = \frac{( y - y ^{2} )}{x}

t a y l or \frac{1 + x}{1 - x} - 1

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

\frac{d}{d x} (9 + 3 x + sin (3 x))

t an g e n t f (x) = 2 x^{- 1}, at x = 5