derivative of 5^{x-1}

解答

\frac{d}{d x} (5^{x - 1})

ln (5) \cdot 5^{x - 1}

求解步骤

\frac{d}{d x} (5^{x - 1})

使用指数法则:

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

5^{x - 1} = e^{(x - 1) l n (5)}

= \frac{d}{d x} (e^{(x - 1) l n (5)})

使用连锁律:

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

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

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

= e^{(x - 1) l n (5)} ln (5)

e^{(x - 1) l n (5)} = 5^{x - 1}

= ln (5) \cdot 5^{x - 1}

d er i v a t i v e G (t) = \frac{4 t}{t + 1}

t an g e n t f (x) = x^{2} + 5 x, at x = 4

\int x e^{- x} - e^{- x} d x

\frac{\partial}{\partial x} (3 e^{3 x})

y^{^{'}} = y (1 - y), y (0) = 8