derivative y=x^53^x

解答

导数

y = x^{5} 3^{x}

5 x^{4} \cdot 3^{x} + 3^{x} ln (3) x^{5}

求解步骤

\frac{d}{d x} (x^{5} \cdot 3^{x})

使用微分乘法定则:

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

f = x^{5}, g = 3^{x}

= \frac{d}{d x} (x^{5}) 3^{x} + \frac{d}{d x} (3^{x}) x^{5}

\frac{d}{d x} (x^{5}) = 5 x^{4}

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

= 5 x^{4} \cdot 3^{x} + 3^{x} ln (3) x^{5}

\int (1 + (\frac{1}{4 x ^{\frac{2}{3}}})) d x

\frac{d y}{d x} = 2 y - 2 y^{5}

\int \frac{ln ( x ) + 1}{x ^{2}} d x

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\int_{0}^{1} (2 x - 1) e^{2 x} d x