derivative of (sqrt(3)^x)

解答

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

\frac{1}{2} ln (3) e^{\frac{l n ( 3 ) x}{2}}

求解步骤

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

化简

(3)^{x} : 3^{\frac{x}{2}}

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

使用指数法则:

a^{b} = e^{b l n (a)}

3^{\frac{x}{2}} = e^{\frac{x}{2} l n (3)}

= \frac{d}{d x} (e^{\frac{x}{2} l n (3)})

使用连锁律:

e^{\frac{x}{2} l n (3)} \frac{d}{d x} (\frac{x}{2} ln (3))

= e^{\frac{x}{2} l n (3)} \frac{d}{d x} (\frac{x}{2} ln (3))

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

= e^{\frac{x}{2} l n (3)} \frac{1}{2} ln (3)

分式相乘:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1}{2} ln (3) e^{\frac{l n ( 3 ) x}{2}}

\int \frac{2 x + 1}{4 x ^{2} + 4 x + 7} d x

f (x) = 3 sin (x)

d er i v a t i v e F (r) = \frac{2}{r ^{3}}

\frac{\partial}{\partial x} (\frac{6}{5} - \frac{6}{5} e^{- 20 t})

\frac{d}{d t} (2 cos (3 t))