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第4章:坐标变换
Lesson: 3.3 Derivative of Logarithm Functions 对数函数的导数
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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)

Answer :
–5cot5x
2. log(x^2 – x)
Answer :
\frac{2x-1}{\left(x^2-x\right)\ln{10}}
3. ln (ln3x^2)
Answer :
\frac{2}{x\ln{3x^2}}
4. \sqrt{xln{x^2}}
Answer :
\frac{\ln{x}+1}{\sqrt{x\ln{x^2}}}
5. ln{(}{sin}^{-1}{\sqrt x})
Answer :
\frac{1}{2\sqrt{x(1-x)}\sin^{-1}{\sqrt x}}
6. sin-1(ln2x)
Answer :
\frac{1}{x\sqrt{1-\left(\ln{2x}\right)^2}}
7. x{tan}^{-1}{x}-ln{\sqrt{1+x^2}}
Answer :
{tan}^{-1}{x}
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第4章:坐标变换
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