derivative of x^{1/2}+4x^{2/3}+7x+3

解答

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

\frac{1}{2 x ^{\frac{1}{2}}} + \frac{8}{3 x ^{\frac{1}{3}}} + 7

求解步骤

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

使用微分加减法定则:

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

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

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

\frac{d}{d x} (4 x^{\frac{2}{3}}) = \frac{8}{3 x ^{\frac{1}{3}}}

\frac{d}{d x} (7 x) = 7

\frac{d}{d x} (3) = 0

= \frac{1}{2 x ^{\frac{1}{2}}} + \frac{8}{3 x ^{\frac{1}{3}}} + 7 + 0

化简

= \frac{1}{2 x ^{\frac{1}{2}}} + \frac{8}{3 x ^{\frac{1}{3}}} + 7

x \to 0 lim (cot (7 x))

\int 9 tan (9 x) d x

\frac{d}{d m} (5 m^{2} + 15 m^{3})

\int \frac{1}{9 e ^{- 5 x} + e ^{5 x}} d x

d er i v a t i v e y = 1 1^{t a n (6 x)}