zs

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

受欢迎的微积分 >

d/(da)(blog_{10}(y/x+(0.6x)/(sqrt(a))))

解答

\frac{d}{d a} (b lo g_{10} (\frac{y}{x} + \frac{0.6 x}{a}))

解答

\frac{0.43429 \dots b ( - 0.3 x ^{2} + a ^{\frac{3}{2}} \frac{d}{d a} ( y ) )}{a ( a y + 0.6 x ^{2} )}

求解步骤

\frac{d}{d a} (b lo g_{10} (\frac{y}{x} + \frac{0.6 x}{a}))

将

b, x

视为常数

将常数提出:

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

= b \frac{d}{d a} (lo g_{10} (\frac{y}{x} + \frac{0.6 x}{a}))

使用对数计算法则:

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

= b \frac{d}{d a} \frac{ln ( \frac{y}{x} + \frac{0.6 x}{a} )}{ln ( 10 )}

将常数提出:

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

= b \frac{1}{ln ( 10 )} \frac{d}{d a} (ln (\frac{y}{x} + \frac{0.6 x}{a}))

使用连锁律:

\frac{1}{\frac{y}{x} + \frac{0.6 x}{a}} \frac{d}{d a} (\frac{y}{x} + \frac{0.6 x}{a})

= \frac{1}{\frac{y}{x} + \frac{0.6 x}{a}} \frac{d}{d a} (\frac{y}{x} + \frac{0.6 x}{a})

\frac{d}{d a} (\frac{y}{x} + \frac{0.6 x}{a}) = \frac{\frac{d}{d a} ( y )}{x} - \frac{0.3 x}{a ^{\frac{3}{2}}}

= b \frac{1}{ln ( 10 )} \cdot \frac{1}{\frac{y}{x} + \frac{0.6 x}{a}} (\frac{\frac{d}{d a} ( y )}{x} - \frac{0.3 x}{a ^{\frac{3}{2}}})

化简

b \frac{1}{ln ( 10 )} \cdot \frac{1}{\frac{y}{x} + \frac{0.6 x}{a}} (\frac{\frac{d}{d a} ( y )}{x} - \frac{0.3 x}{a ^{\frac{3}{2}}}) : \frac{0.43429 \dots b ( - 0.3 x ^{2} + a ^{\frac{3}{2}} \frac{d}{d a} ( y ) )}{a ( a y + 0.6 x ^{2} )}

= \frac{0.43429 \dots b ( - 0.3 x ^{2} + a ^{\frac{3}{2}} \frac{d}{d a} ( y ) )}{a ( a y + 0.6 x ^{2} )}

流行的例子

面积 y=x^{4/3},y=2x^{1/3}

a re a y = x^{\frac{4}{3}}, y = 2 x^{\frac{1}{3}}

integral of x/6

\int \frac{x}{6} d x

integral of 1/(x^2-8x+20)

\int \frac{1}{x ^{2} - 8 x + 20} d x

integral of e^{-sx}

\int e^{- s x} d x

derivative of (x^4/8+(x^{-2})/4)

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