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derivative y=log_{4}(x)+log_{4}(x^2)

解答

导数

y = lo g_{4} (x) + lo g_{4} (x^{2})

解答

\frac{3}{2 ln ( 2 ) x}

求解步骤

\frac{d}{d x} (lo g_{4} (x) + lo g_{4} (x^{2}))

化简

lo g_{4} (x) + lo g_{4} (x^{2}) : lo g_{4} (x^{3})

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

使用对数计算法则:

lo g_{a} (b) = \frac{ln ( b )}{ln ( a )}

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

将常数提出:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{1}{ln ( 4 )} \frac{d}{d x} (ln (x^{3}))

使用连锁律:

\frac{1}{x ^{3}} \frac{d}{d x} (x^{3})

= \frac{1}{x ^{3}} \frac{d}{d x} (x^{3})

\frac{d}{d x} (x^{3}) = 3 x^{2}

= \frac{1}{ln ( 4 )} \cdot \frac{1}{x ^{3}} \cdot 3 x^{2}

化简

\frac{1}{ln ( 4 )} \cdot \frac{1}{x ^{3}} \cdot 3 x^{2} : \frac{3}{2 ln ( 2 ) x}

= \frac{3}{2 ln ( 2 ) x}

作图

流行的例子

derivative of sqrt(x^2-8)

\frac{d}{d x} (x^{2} - 8)

斜率 (0,2),(2,-3)

s l o p e (0, 2), (2, - 3)

laplacetransform \delta(x)

l a pl a ce t r an s f or m δ (x)

泰勒 x^2e^{x-1}1

t a y l or x^{2} e^{x - 1} 1

laplacetransform e^{-2t}

l a pl a ce t r an s f or m e^{- 2 t}