derivative f(x)=x^{3/2}+sqrt(x+4)

解答

导数

f (x) = x^{\frac{3}{2}} + x + 4

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

求解步骤

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

使用微分加减法定则:

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

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

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

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

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

t an g e n t x e^{x}

x \to 0 lim (tan (4 x))

y^{^{''}} - 4 y^{^{'}} - 5 y = 0, y (- 1) = 3, y^{^{'}} (- 1) = 9

\frac{d}{d x} (4 e^{4 e^{x} + x})

d er i v a t i v e f (x) = \frac{- x ^{2} - 4}{( x ^{2} - 4 ) ^{2}}