derivative y=x^{2^x}

解答

导数

y = x^{2^{x}}

x^{2^{x}} (ln (2) \cdot 2^{x} ln (x) + \frac{2 ^{x}}{x})

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

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

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

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

(x^{5} + 3 y) d x - x d y = 0

\int \frac{x ^{3}}{49 + x ^{8}} d x

\frac{d ^{2}}{d x ^{2}} (15 e^{x^{2}})

t an g e n t 9 - x^{2}

\frac{\partial}{\partial x} ((2 x + 6 y)^{11})