derivative x^{2*x}

解答

导数

x^{2 \cdot x}

2 x^{2 x} (ln (x) + 1)

求解步骤

\frac{d}{d x} (x^{2 x})

使用指数法则:

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

x^{2 x} = e^{2 x l n (x)}

= \frac{d}{d x} (e^{2 x l n (x)})

使用连锁律:

e^{2 x l n (x)} \frac{d}{d x} (2 x ln (x))

= e^{2 x l n (x)} \frac{d}{d x} (2 x ln (x))

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

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

e^{2 x l n (x)} = x^{2 x}

= 2 x^{2 x} (ln (x) + 1)

d er i v a t i v e y = (x^{4} + 5 x^{2})^{7}

d er i v a t i v e y - x^{2} + 1

\frac{d}{d t} (50 + 4 t)

d er i v a t i v e 3 - 2 x + 4 x^{2}

d er i v a t i v e 9 e^{- 3} x^{2}