derivative y=sqrt(x)^{7x}

解答

导数

y = x^{7 x}

7 (x)^{7 x} (ln (x) + \frac{1}{2})

求解步骤

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

使用指数法则:

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

(x)^{7 x} = e^{7 x l n (x)}

= \frac{d}{d x} (e^{7 x l n (x)})

使用连锁律:

e^{7 x l n (x)} \frac{d}{d x} (7 x ln (x))

= e^{7 x l n (x)} \frac{d}{d x} (7 x ln (x))

\frac{d}{d x} (7 x ln (x)) = 7 (ln (x) + \frac{1}{2})

= e^{7 x l n (x)} \cdot 7 (ln (x) + \frac{1}{2})

e^{7 x l n (x)} = (x)^{7 x}

= 7 (x)^{7 x} (ln (x) + \frac{1}{2})

l a pl a ce t r an s f or m t^{3} e^{- 3 t}

x \to 0 lim (6^{x})

\frac{\partial}{\partial x} (x^{3} y^{7})

l a pl a ce t r an s f or m - 5 t^{2} e^{- 4 t} + sin (3 t)

\frac{d}{d x} (x^{3} - 7 x^{2} + 14 x - 6)