derivative x^{10x}

解答

导数

x^{10 x}

10 x^{10 x} (ln (x) + 1)

求解步骤

\frac{d}{d x} (x^{10 x})

使用指数法则:

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

x^{10 x} = e^{10 x l n (x)}

= \frac{d}{d x} (e^{10 x l n (x)})

使用连锁律:

e^{10 x l n (x)} \frac{d}{d x} (10 x ln (x))

= e^{10 x l n (x)} \frac{d}{d x} (10 x ln (x))

\frac{d}{d x} (10 x ln (x)) = 10 (ln (x) + 1)

= e^{10 x l n (x)} \cdot 10 (ln (x) + 1)

e^{10 x l n (x)} = x^{10 x}

= 10 x^{10 x} (ln (x) + 1)

d er i v a t i v e 3 x + 10

\int (- \frac{1}{5} sec (1 - 5 x)) d x

x \to 1 lim ((ln (x))^{1 - x})

\int e^{14 x} d x

\frac{d}{d x} ((x^{2} + 3) (x^{2} - 4 x))