3.3 Derivative of Logarithm Functions 对数函数的导数 - 独中课程 | 线上补习

高三数学 | 高级数学

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3.3 Derivative of Logarithm Functions 对数函数的导数

Differentiate the following statement
微分下列各式

1. ln(csc5x)

–5cot5x

2. log(x $^2$ – x)

$\frac{2x-1}{\left(x^2-x\right)\ln{10}}$

3. ln (ln3x $^2$ )

$\frac{2}{x\ln{3x^2}}$

4. $\sqrt{xln{x^2}}$

$\frac{\ln{x}+1}{\sqrt{x\ln{x^2}}}$

5. $ln{(}{sin}^{-1}{\sqrt x})$

$\frac{1}{2\sqrt{x(1-x)}\sin^{-1}{\sqrt x}}$

6. $sin-1(ln2x)$

$\frac{1}{x\sqrt{1-\left(\ln{2x}\right)^2}}$

7. $x{tan}^{-1}{x}-ln{\sqrt{1+x^2}}$

${tan}^{-1}{x}$