(12lnx)′=12×1x=12x\left( \frac{1}{2} \ln x \right)' = \frac{1}{2} \times \frac{1}{x} = \frac{1}{2x}(21lnx)′=21×x1=2x1 所以,函数 lnx\ln\sqrt{x}lnx 的导数为 12x\frac{1}{2x}2x1。 例题: 求lnt\ln\sqrt{t}lnt 在t=4t = 4t=4 处的导数值。
=ln(\sqrt{1+x^2}+x)^2 =2ln(\sqrt{1+x^2}+x) 所以 y'=2\frac{(\sqrt{1+x^2}+x)'}{\sqrt{1+x^2}+x} =2\frac{\frac{x}{\sqrt{1+x^2}}+1 }{\sqrt{1+x^2}+x} =2\frac{\frac{x+\sqrt{1+x^2}}{\sqrt{1+x^2}} }{\sqrt{1+x^2}+x} =\frac{...
$y'=\dfrac {1} {\sqrt {1-{x}^{2}}}$$\left ( {\sqrt {1-{x}^{2}}} \right )'$ $= 1 (√ (1-x^2))\times 1 (2√ (1-x^2))\left ( {1-{x}^{2}} \right )'$ $= 1 (2 ( (1-x^2) ))\left ( {-2x} \right )$ $=$$\dfrac {x} {{x}^{2}-1}$, ...
求导:y=ln√(1-x^2)y= \ln \sqrt{1-x^{2}}. 相关知识点: 试题来源: 解析 由题意得:y'=1/(√(1-x^2))(√(1-x^2))^1=1/(√(1-x^2))x2√(1-x^2)(1-x^2)'=1/(2(1-x^2)^2)(-2x)=x/(x^2-1),综上所述,y'=x/(x^2-1). ...
(4)y'=2^x⋅ ln 2,y''=2^x⋅ (ln 2)^2, (5)y'=2xln x+x^2⋅ 1x=2xln x+x,y''=2ln x+2x⋅ 1x+1=2ln x+2+2=3+2ln x; (6)y=(x-1)(x+1)=(x+1-2)(x+1)=1-2(x+1), 则y'=2((x+1)^2),y''=-4((x+1)^3). 根据导数的公式进行求导即...
(1)要使$y=\ln \left(x^{2}-x\right)$有意义,可得$x^{2}-x \gt 0$,解得$x \lt 0$或$x \gt 1$;函数的定义域为:$\left\{x\left|\right.x \lt 0或x \gt 1\right\}$.(2)要使$y=\sqrt {\ln x}$有意义,可得$\ln x\geqslant 0$,解得$x\geqslant 1$;函数的定义域为:$\lef...
$\left(2\right)$$f'\left(x\right)=7$; $\left(3\right)f'(x)=1x-sin x\left(x\gt 0\right)$; $\left(4\right)$$f'\left(x\right)=-\cos x$; $\left(5\right)f'(x)=1(2√x)\left(x\gt 0\right)$; $\left(6\right)$$f'\left(x\right)=-\dfrac{...
7、常用的对数运算法则:常用的对数运算法则有六条,包括:$$\log_a ab = \log_a a + \log_a b \\ \log_a \frac{a}{b} = \log_a a - \log_a b \\ \log_a a^b = b\log_a a \\ \log_a \sqrt[x]{a} = \frac{1}{x}\log_a a \\ \log_a a^m\times a^n = (m + n...
11.下列函数求导正确的个数是( ) (1 )y=ln3,则y{\;}^'=\frac{1}{3}y=ln3,则y{\;}^'=\frac{1}{3} (2)y=\sqrt{2x-1},则{y^'}=\frac{1}{{\sqrt{2x-1}}}\sqrt{2x-1},则{y^'}=\frac{1}{{\sqrt{2x-1}}} (3)y=e2x+1,则y′=2e2x+1 ...
ln(1+2)=∫02dx1+x=∫022dx1+x+∫222dx1+x>∫022dx1+22+∫222dx1+2=22....