derivative of 8^{x^4}

解答

\frac{d}{d x} (8^{x^{4}})

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

求解步骤

\frac{d}{d x} (8^{x^{4}})

使用指数法则:

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

8^{x^{4}} = e^{x^{4} l n (8)}

= \frac{d}{d x} (e^{x^{4} l n (8)})

使用连锁律:

e^{x^{4} l n (8)} \frac{d}{d x} (x^{4} ln (8))

= e^{x^{4} l n (8)} \frac{d}{d x} (x^{4} ln (8))

\frac{d}{d x} (x^{4} ln (8)) = 12 ln (2) x^{3}

= e^{x^{4} l n (8)} \cdot 12 ln (2) x^{3}

化简

e^{x^{4} l n (8)} \cdot 12 ln (2) x^{3} : 3 ln (2) \cdot 2^{3 x^{4} + 2} x^{3}

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

a re a \frac{x}{1 + x ^{2}}, \frac{x ^{2}}{1 + x ^{3}}, [0, 1]

\int \frac{8}{4 + 8 x} d x

d er i v a t i v e \frac{180}{x ^{7}} - \frac{4}{x ^{3}}

\frac{d y}{d x} = (e^{x} - e^{- x})^{2}

t an g e n t f (x) = x^{2}, (0, - 9)