Given: \(\displaystyle{x}{y}^{{{''}}}+{\left({2}+{2}{x}\right)}{y}^{{'}}+{2}{y}={0}\) has a solution \(\displaystyle{y}_{{{1}}}{\left({x}\right)}={x}^{{-{1}}}\),

What is the derivative of the work function?

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How to differentiate $y=\log <!--\; \; -->x^2$?

The solution of a differential equation y′′+3y′+2y=0 is of the form
A) $c_1{e}^x+c_2{e}^{2x}$
B) $c_1{e}^{-<!--\; -\; -->x}+c_2{e}^{3x}$
C) $c_1{e}^{-<!--\; -\; -->x}+c_2{e}^{-<!--\; -\; -->2x}$
D) $c_1{e}^{-<!--\; -\; -->2x}+c_2{2}^{-<!--\; -\; -->x}$

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How to implicitly differentiate ${\displaystyle \sqrt{xy}=x-2y}$?

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How to find the sum of the infinite geometric series given ${\displaystyle 1+\frac{2}{3}+\frac{4}{9}+...}$?

Look at this series: 1.5, 2.3, 3.1, 3.9, ... What number should come next?
A. 4.2
B. 4.4
C. 4.7
D. 5.1

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How to differentiate ${\displaystyle x^{\frac{2}{3}}+y^{\frac{2}{3}}=4}$?

The differential coefficient of $\sec \left({\tan }^{-1}\left(x\right)\right)$.