ja

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

人気のある微分積分 >

derivative y=log_{5}(x^4-7)

解

導関数

y = lo g_{5} (x^{4} - 7)

解

\frac{4 x ^{3}}{ln ( 5 ) ( x ^{4} - 7 )}

解答ステップ

\frac{d}{d x} (lo g_{5} (x^{4} - 7))

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 ( x ^{4} - 7 )}{ln ( 5 )})

定数を除去:

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

= \frac{1}{ln ( 5 )} \frac{d}{d x} (ln (x^{4} - 7))

連鎖法則を適用:

\frac{1}{x ^{4} - 7} \frac{d}{d x} (x^{4} - 7)

= \frac{1}{x ^{4} - 7} \frac{d}{d x} (x^{4} - 7)

\frac{d}{d x} (x^{4} - 7) = 4 x^{3}

= \frac{1}{ln ( 5 )} \cdot \frac{1}{x ^{4} - 7} \cdot 4 x^{3}

簡素化

\frac{1}{ln ( 5 )} \cdot \frac{1}{x ^{4} - 7} \cdot 4 x^{3} : \frac{4 x ^{3}}{ln ( 5 ) ( x ^{4} - 7 )}

= \frac{4 x ^{3}}{ln ( 5 ) ( x ^{4} - 7 )}

グラフ

人気の例

tangent y=x^3-9x,(1,-8)

t an g e n t y = x^{3} - 9 x, (1, - 8)

(\partial)/(\partial y)(-e^{-xy^2}*y^2)

\frac{\partial}{\partial y} (- e^{- x y^{2}} \cdot y^{2})

(\partial)/(\partial x)(e^{sin(x^2)})

\frac{\partial}{\partial x} (e^{s i n (x^{2})})

integral of (5arcsin(x))/(x^2)

\int \frac{5 arcsin ( x )}{x ^{2}} d x

x^3y^'+2x^2y=-3cos(3x)y^{-1/2}

x^{3} y^{^{'}} + 2 x^{2} y = - 3 cos (3 x) y^{- \frac{1}{2}}