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人気のある微分積分 >

derivative of 5log_{10}(4x^2)

解

\frac{d}{d x} (5 lo g_{10} (4 x^{2}))

解

\frac{10}{ln ( 10 ) x}

解答ステップ

\frac{d}{d x} (5 lo g_{10} (4 x^{2}))

定数を除去:

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

= 5 \frac{d}{d x} (lo g_{10} (4 x^{2}))

対数の規則を適用する:

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

= 5 \frac{d}{d x} (\frac{ln ( 4 x ^{2} )}{ln ( 10 )})

定数を除去:

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

= 5 \cdot \frac{1}{ln ( 10 )} \frac{d}{d x} (ln (4 x^{2}))

連鎖法則を適用:

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

= \frac{1}{4 x ^{2}} \frac{d}{d x} (4 x^{2})

\frac{d}{d x} (4 x^{2}) = 8 x

= 5 \cdot \frac{1}{ln ( 10 )} \cdot \frac{1}{4 x ^{2}} \cdot 8 x

簡素化

5 \cdot \frac{1}{ln ( 10 )} \cdot \frac{1}{4 x ^{2}} \cdot 8 x : \frac{10}{ln ( 10 ) x}

= \frac{10}{ln ( 10 ) x}

グラフ

人気の例

integral of csc^3(4x)

\int csc^{3} (4 x) d x

derivative of (ln(x^3)/(ln(x^2)))

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

integral of (3x+11)/(x^2-x-6)

\int \frac{3 x + 11}{x ^{2} - x - 6} d x

勾配 y=-5x^{1/2}+x^{3/2}

s l o p e y = - 5 x^{\frac{1}{2}} + x^{\frac{3}{2}}

derivative of (x^2+3x-1e^x)

\frac{d}{d x} ((x^{2} + 3 x - 1) e^{x})