derivative of 6^{3x-4}

解答

\frac{d}{d x} (6^{3 x - 4})

ln (6) \cdot 2^{3 x - 4} \cdot 3^{3 x - 3}

求解步骤

\frac{d}{d x} (6^{3 x - 4})

使用指数法则:

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

6^{3 x - 4} = e^{(3 x - 4) l n (6)}

= \frac{d}{d x} (e^{(3 x - 4) l n (6)})

使用连锁律:

e^{(3 x - 4) l n (6)} \frac{d}{d x} ((3 x - 4) ln (6))

= e^{(3 x - 4) l n (6)} \frac{d}{d x} ((3 x - 4) ln (6))

\frac{d}{d x} ((3 x - 4) ln (6)) = 3 ln (6)

= e^{(3 x - 4) l n (6)} \cdot 3 ln (6)

化简

e^{(3 x - 4) l n (6)} \cdot 3 ln (6) : ln (6) \cdot 2^{3 x - 4} \cdot 3^{3 x - 3}

= ln (6) \cdot 2^{3 x - 4} \cdot 3^{3 x - 3}

\int_{0}^{x} sin (\frac{π}{2} t^{2}) d t

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

\int_{0}^{1} x^{2} - x d x

d er i v a t i v e y = \frac{x + 1}{x - 2}

\frac{d}{d x} (9 + x + y^{2})