derivative of x^2log_{2}(7-6x)

解答

\frac{d}{d x} (x^{2} lo g_{2} (7 - 6 x))

\frac{- 6 x ^{2} + 2 x ln ( 7 - 6 x ) ( 7 - 6 x )}{ln ( 2 ) ( 7 - 6 x )}

求解步骤

\frac{d}{d x} (x^{2} lo g_{2} (7 - 6 x))

使用微分乘法定则:

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

f = x^{2}, g = lo g_{2} (7 - 6 x)

= \frac{d}{d x} (x^{2}) lo g_{2} (7 - 6 x) + \frac{d}{d x} (lo g_{2} (7 - 6 x)) x^{2}

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

\frac{d}{d x} (lo g_{2} (7 - 6 x)) = - \frac{6}{ln ( 2 ) ( 7 - 6 x )}

= 2 x lo g_{2} (7 - 6 x) + (- \frac{6}{ln ( 2 ) ( 7 - 6 x )}) x^{2}

化简

2 x lo g_{2} (7 - 6 x) + (- \frac{6}{ln ( 2 ) ( 7 - 6 x )}) x^{2} : \frac{- 6 x ^{2} + 2 x ln ( 7 - 6 x ) ( 7 - 6 x )}{ln ( 2 ) ( 7 - 6 x )}

= \frac{- 6 x ^{2} + 2 x ln ( 7 - 6 x ) ( 7 - 6 x )}{ln ( 2 ) ( 7 - 6 x )}

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