# Calculate: y=x^2sqrt(8x-5)

## Expression: $y={x}^{2}\sqrt{ 8x-5 }$

Take the derivative of both sides

$y '=\frac{ \mathrm{d} }{ \mathrm{d}x} \left( {x}^{2}\sqrt{ 8x-5 } \right)$

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

$y '=\frac{ 20{x}^{2}-10x }{ \sqrt{ 8x-5 } }$

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