derivative of 2x^{3x}

解答

\frac{d}{d x} (2 x^{3 x})

6 x^{3 x} (ln (x) + 1)

求解步骤

\frac{d}{d x} (2 x^{3 x})

将常数提出:

(a \cdot f)^{'} = a \cdot f^{'}

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

使用指数法则:

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

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

= 2 \frac{d}{d x} (e^{3 x l n (x)})

使用连锁律:

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

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

\frac{d}{d x} (3 x ln (x)) = 3 (ln (x) + 1)

= 2 e^{3 x l n (x)} \cdot 3 (ln (x) + 1)

化简

2 e^{3 x l n (x)} \cdot 3 (ln (x) + 1) : 6 x^{3 x} (ln (x) + 1)

= 6 x^{3 x} (ln (x) + 1)

\frac{\partial}{\partial x} (\frac{1}{2} (x - y)^{2})

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\frac{d}{d x} (2 sin^{3} (x) - 3 cos^{2} (x))

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