derivative of (2x^{3x})

解答

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

3 ln (2) \cdot 8^{x} x^{3 x} + 3 x^{3 x} (ln (x) + 1) \cdot 8^{x}

求解步骤

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

化简

(2 x)^{3 x} : 8^{x} x^{3 x}

= \frac{d}{d x} (8^{x} x^{3 x})

使用微分乘法定则:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = 8^{x}, g = x^{3 x}

= \frac{d}{d x} (8^{x}) x^{3 x} + \frac{d}{d x} (x^{3 x}) 8^{x}

\frac{d}{d x} (8^{x}) = 3 ln (2) \cdot 8^{x}

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

= 3 ln (2) \cdot 8^{x} x^{3 x} + 3 x^{3 x} (ln (x) + 1) \cdot 8^{x}

\frac{d}{d x} (5 x - 9)

y^{^{''}} - 5 y^{^{'}} + 6 y = sin (x)

\int sec^{2} (3 θ) d θ

x \to 8 - lim (\frac{x}{ln ( 9 - x )})

\frac{d}{d x} (arctan (x - 1))