derivative of (sqrt(5)^x)

解答

\frac{d}{d x} ((5)^{x})

\frac{1}{2} ln (5) e^{\frac{l n ( 5 ) x}{2}}

求解步骤

\frac{d}{d x} ((5)^{x})

化简

(5)^{x} : 5^{\frac{x}{2}}

= \frac{d}{d x} (5^{\frac{x}{2}})

使用指数法则:

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

5^{\frac{x}{2}} = e^{\frac{x}{2} l n (5)}

= \frac{d}{d x} (e^{\frac{x}{2} l n (5)})

使用连锁律:

e^{\frac{x}{2} l n (5)} \frac{d}{d x} (\frac{x}{2} ln (5))

= e^{\frac{x}{2} l n (5)} \frac{d}{d x} (\frac{x}{2} ln (5))

\frac{d}{d x} (\frac{x}{2} ln (5)) = \frac{1}{2} ln (5)

= e^{\frac{x}{2} l n (5)} \frac{1}{2} ln (5)

分式相乘:

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

= \frac{1}{2} ln (5) e^{\frac{l n ( 5 ) x}{2}}

(2 t^{2} + 1)^{^{'}}

\frac{d}{d x} (14 e^{x})

\int arccot (3 x) d x

y^{^{'}} + y = 6

t an g e n t y = \frac{x}{x + 3}, (1, 2)