$y '=\frac{ \mathrm{d} }{ \mathrm{d}x} \left( {x}^{2}\sqrt{ 8x-5 } \right)$
Use differentiation rule $\frac{ \mathrm{d} }{ \mathrm{d}x} \left( f \times g \right)=\frac{ \mathrm{d} }{ \mathrm{d}x} \left( f \right) \times g+f \times \frac{ \mathrm{d} }{ \mathrm{d}x} \left( g \right)$$y '=\frac{ \mathrm{d} }{ \mathrm{d}x} \left( {x}^{2} \right) \times \sqrt{ 8x-5 }+{x}^{2} \times \frac{ \mathrm{d} }{ \mathrm{d}x} \left( \sqrt{ 8x-5 } \right)$
Find the derivative$y '=2x\sqrt{ 8x-5 }+{x}^{2} \times \frac{ \mathrm{d} }{ \mathrm{d}x} \left( \sqrt{ 8x-5 } \right)$
Find the derivative of the composite function$y '=2x\sqrt{ 8x-5 }+{x}^{2} \times \frac{ 1 }{ 2\sqrt{ 8x-5 } } \times 8$
Simplify the expression$y '=\frac{ 20{x}^{2}-10x }{ \sqrt{ 8x-5 } }$