derivative x^{x^3}

解答

导数

x^{x^{3}}

x^{x^{3}} (3 x^{2} ln (x) + x^{2})

求解步骤

\frac{d}{d x} (x^{x^{3}})

使用指数法则:

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

x^{x^{3}} = e^{x^{3} l n (x)}

= \frac{d}{d x} (e^{x^{3} l n (x)})

使用连锁律:

e^{x^{3} l n (x)} \frac{d}{d x} (x^{3} ln (x))

= e^{x^{3} l n (x)} \frac{d}{d x} (x^{3} ln (x))

\frac{d}{d x} (x^{3} ln (x)) = 3 x^{2} ln (x) + x^{2}

= e^{x^{3} l n (x)} (3 x^{2} ln (x) + x^{2})

e^{x^{3} l n (x)} = x^{x^{3}}

= x^{x^{3}} (3 x^{2} ln (x) + x^{2})

l c m f (x) =, 4 at x

\frac{d}{d y} (6 y^{2})

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