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人気のある微分積分 >

derivative y=log_{3}(5x^4)

解

導関数

y = lo g_{3} (5 x^{4})

解

\frac{4}{ln ( 3 ) x}

解答ステップ

\frac{d}{d x} (lo g_{3} (5 x^{4}))

対数の規則を適用する:

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

= \frac{d}{d x} (\frac{ln ( 5 x ^{4} )}{ln ( 3 )})

定数を除去:

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

= \frac{1}{ln ( 3 )} \frac{d}{d x} (ln (5 x^{4}))

連鎖法則を適用:

\frac{1}{5 x ^{4}} \frac{d}{d x} (5 x^{4})

= \frac{1}{5 x ^{4}} \frac{d}{d x} (5 x^{4})

\frac{d}{d x} (5 x^{4}) = 20 x^{3}

= \frac{1}{ln ( 3 )} \cdot \frac{1}{5 x ^{4}} \cdot 20 x^{3}

簡素化

\frac{1}{ln ( 3 )} \cdot \frac{1}{5 x ^{4}} \cdot 20 x^{3} : \frac{4}{ln ( 3 ) x}

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

グラフ

人気の例

implicit 2x^2+y^2-7=0

im pl i c i t 2 x^{2} + y^{2} - 7 = 0

limit as x approaches 1 of (x-x^3)/(x-1)

x \to 1 lim (\frac{x - x ^{3}}{x - 1})

derivative of (d^2/(dx^2)(x^4)+cos(x)+1)

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

integral of 3x^3e^{5x^4}

\int 3 x^{3} e^{5 x^{4}} d x

y^{''}+3y^'-10y=0

y^{^{''}} + 3 y^{^{'}} - 10 y = 0