Question

find the derivative of x²+1/x²​

Answer 1

Step-by-step explanation:

$Let \: \: y = {x}^{2} + \frac{1}{ {x}^{2} } \\ differentiating \: w.r.t. \: x \: both \: sides : \\ \\ \frac{dy}{dx} = \frac{d}{dx} ({x}^{2} + \frac{1}{ {x}^{2} }) \\ \\ = \frac{d}{dx} {x}^{2} + \frac{d}{dx} {x}^{ - 2} \\ \\ = 2x \times \frac{d}{dx} \: x + ( - 2) \times {x}^{ - 2 - 1} \times \frac{d}{dx} {x} \\ \\ = 2x \times 1 - 2 {x}^{ - 3}\times 1 \\ \\ = 2x - 2 {x}^{ - 3} \\ \\ = 2x - \frac{2}{ {x}^{ 3} } \\ \\ = \frac{2( {x}^{4} - 1)}{ {x}^{3} } \\ \\ = \frac{2( {x}^{2} + 1)( {x}^{2} - 1)}{ {x}^{3} } \\ \\ = \frac{2( {x}^{2} + 1)( {x} + 1)( {x} - 1)}{ {x}^{3} } \\ \\ thus \\ \\ \purple { \boxed{\frac{dy}{dx} ({x}^{2} + \frac{1}{ {x}^{2} }) = \frac{2( {x}^{2} + 1)( {x} + 1)( {x} - 1)}{ {x}^{3} }}}$

Answer 2

Answer:

Sheep and goats were first domesticated roughly 11,000 years ago. These are called beasts of burden. The primary animal to be tamed or domesticated was a Goat. Afterward the first humans started domesticating wolves which then developed to Dogs