Question

find the derivative of x^-2 + x^2 with respect to x​

Answer 1

Question

Find the derivative of the following w.r.t to x

$\large{ \sf{ {x}^{ - 2} + {x}^{2} }}$

Solution

Given Expression,

$\large{ \sf{y = {x}^{ - 2} + {x}^{2} }}$

To find

Derivative of the above equation w.r.t to x

Power Rule

$\large{ \tt{ {x}^{n} } = n {x}^{n - 1} }$

Now,

$\sf{y' = \frac{d( {x}^{ - 2} + {x}^{2} ) }{dx} } \\ \\ \implies \: \sf{y' = \frac{d( {x}^{ - 2} )}{dx} + \frac{d(x {}^{2} )}{dx} } \\ \\ \large{\implies \: \boxed{ \boxed{\sf{y' = 2x - 2 {x}^{ - 3} }}}}$

Answer 2

Solution

$\sf{y' = \frac{d( {x}^{ - 2} + {x}^{2} ) }{dx} } \\ \\ \implies \: \sf{y' = \frac{d( {x}^{ - 2} )}{dx} + \frac{d(x {}^{2} )}{dx} } \\ \\ \large{\implies \: \boxed{ \boxed{\sf{y' = 2x - 2 {x}^{ - 3} }}}}$