derivative (1/2)^{x-1}+3

解答

导数

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

- ln (2) (\frac{1}{2})^{x - 1}

求解步骤

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

使用微分加减法定则:

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

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

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

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

= - ln (2) (\frac{1}{2})^{x - 1} + 0

化简

= - ln (2) (\frac{1}{2})^{x - 1}

\int \frac{x ^{3}}{a ^{2} - x ^{2}} d x

d er i v a t i v e \frac{t ^{5} - 3 t ^{2}}{2 t}

\int \frac{x}{x + 5} d x

d er i v a t i v e f (x) = 7 e^{- x} - 4 e^{- 7 x}

\frac{\partial}{\partial x} (3 sec^{2} (3 x - 2 y + 1))