derivative of 7^xlog_{7}(x)

解答

\frac{d}{d x} (7^{x} lo g_{7} (x))

7^{x} ln (x) + \frac{7 ^{x}}{ln ( 7 ) x}

求解步骤

\frac{d}{d x} (7^{x} lo g_{7} (x))

使用微分乘法定则:

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

f = 7^{x}, g = lo g_{7} (x)

= \frac{d}{d x} (7^{x}) lo g_{7} (x) + \frac{d}{d x} (lo g_{7} (x)) 7^{x}

\frac{d}{d x} (7^{x}) = 7^{x} ln (7)

\frac{d}{d x} (lo g_{7} (x)) = \frac{1}{x ln ( 7 )}

= 7^{x} ln (7) lo g_{7} (x) + \frac{1}{x ln ( 7 )} \cdot 7^{x}

化简

7^{x} ln (7) lo g_{7} (x) + \frac{1}{x ln ( 7 )} \cdot 7^{x} : 7^{x} ln (x) + \frac{7 ^{x}}{ln ( 7 ) x}

= 7^{x} ln (x) + \frac{7 ^{x}}{ln ( 7 ) x}

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