derivative y=x^x

解答

导数

y = x^{x}

x^{x} (ln (x) + 1)

求解步骤

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

使用指数法则:

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

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

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

使用连锁律:

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

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

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

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

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

= x^{x} (ln (x) + 1)

d er i v a t i v e y = ln (2 x)

c a r t es ian (2, \frac{3 π}{2})

d er i v a t i v e f (x) = 5 x e^{x^{2} - 3}

p o l a r (5, 53)

l in e (0, 3), (2, - 3)