derivative x^4e^{6x}

解答

导数

x^{4} e^{6 x}

4 x^{3} e^{6 x} + e^{6 x} \cdot 6 x^{4}

求解步骤

\frac{d}{d x} (x^{4} e^{6 x})

使用微分乘法定则:

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

f = x^{4}, g = e^{6 x}

= \frac{d}{d x} (x^{4}) e^{6 x} + \frac{d}{d x} (e^{6 x}) x^{4}

\frac{d}{d x} (x^{4}) = 4 x^{3}

\frac{d}{d x} (e^{6 x}) = e^{6 x} \cdot 6

= 4 x^{3} e^{6 x} + e^{6 x} \cdot 6 x^{4}

\frac{d ^{3} y}{d x ^{3}} + \frac{d ^{2} y}{d x ^{2}} - 2 y = 0

\int cos (n) x d x

t an g e n t y = 2 x^{3} - x^{2} + \frac{4}{x}, (4, 1)

x y^{^{''}} + y^{^{'}} = 4 x

y^{^{'}} = 2 (1 + y^{2})