derivative f(s)=8^{sqrt(2s-1)}

解答

导数

f (s) = 8^{2 s - 1}

\frac{3 ln ( 2 ) \cdot 8 ^{2 s - 1}}{2 s - 1}

求解步骤

\frac{d}{d s} (8^{2 s - 1})

使用指数法则:

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

8^{2 s - 1} = e^{2 s - 1 l n (8)}

= \frac{d}{d s} (e^{2 s - 1 l n (8)})

使用连锁律:

e^{2 s - 1 l n (8)} \frac{d}{d s} (2 s - 1 ln (8))

= e^{2 s - 1 l n (8)} \frac{d}{d s} (2 s - 1 ln (8))

\frac{d}{d s} (2 s - 1 ln (8)) = \frac{3 ln ( 2 )}{2 s - 1}

= e^{2 s - 1 l n (8)} \frac{3 ln ( 2 )}{2 s - 1}

化简

e^{2 s - 1 l n (8)} \frac{3 ln ( 2 )}{2 s - 1} : \frac{3 ln ( 2 ) \cdot 8 ^{2 s - 1}}{2 s - 1}

= \frac{3 ln ( 2 ) \cdot 8 ^{2 s - 1}}{2 s - 1}

x \to \infty lim (- \frac{5}{x})

\frac{d}{d x} (\frac{x - 7}{x - 7})

\frac{d}{d x} (g (h, x) (h (x)))

\int_{0}^{2} x e^{4 x} d x

y^{^{'}} = y^{3}, y (0) = 1