Question

differtiation of y= (x⁵/2) - (5/x²)​

Answer 1

$\boxed{y = \dfrac{ {x}^{5} }{2} - \dfrac{5}{ {x}^{2} } }$

Now, differentiation with respect to x :

$\implies \: \dfrac{dy}{dx} = \dfrac{d( \frac{ {x}^{5} }{2}) }{dx} - \dfrac{d( \frac{5}{ {x}^{2} }) }{dx}$

$\implies \: \dfrac{dy}{dx} = \dfrac{1}{2} \dfrac{d( {x}^{5} ) }{dx} - 5\dfrac{d( {x}^{ - 2} )}{dx}$

$\implies \: \dfrac{dy}{dx} = \dfrac{1}{2} (5 {x}^{5 - 1}) + 5(2 {x}^{ - 2 - 1} )$

$\implies \: \dfrac{dy}{dx} = \dfrac{5 {x}^{4} }{2} + 10 {x}^{ - 3}$

So, final answer is:

$\boxed{ \bf \: \dfrac{dy}{dx} = \dfrac{5 {x}^{4} }{2} + 10 {x}^{ - 3} }$