Obtain the derivative of the following function: f(x)=(2e^4x)/(√x)

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Answer to a math question Obtain the derivative of the following function: f(x)=(2e^4x)/(√x)

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$f '\left( x \right)=\frac{ \mathrm{d} }{ \mathrm{d}x} \left( \frac{ 2{e}^{4x} }{ \sqrt{ x } } \right)$

$f '\left( x \right)=\frac{ \frac{ \mathrm{d} }{ \mathrm{d}x} \left( 2{e}^{4x} \right) \times \sqrt{ x }-2{e}^{4x} \times \frac{ \mathrm{d} }{ \mathrm{d}x} \left( \sqrt{ x } \right) }{ {\sqrt{ x }}^{2} }$

$f '\left( x \right)=\frac{ 2{e}^{4x} \times 4\sqrt{ x }-2{e}^{4x} \times \frac{ \mathrm{d} }{ \mathrm{d}x} \left( \sqrt{ x } \right) }{ {\sqrt{ x }}^{2} }$

$f '\left( x \right)=\frac{ 2{e}^{4x} \times 4\sqrt{ x }-2{e}^{4x} \times \frac{ 1 }{ 2\sqrt{ x } } }{ {\sqrt{ x }}^{2} }$

$f '\left( x \right)=\frac{ 8x{e}^{4x}-{e}^{4x} }{ \sqrt{ x }x }$

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