Find the equation of the tangent line to

'y = \frac{x}{e^{2x}} @ (1,\frac{1}{e^{2}})'

Used quotient rule

y' = \frac{e^{2x}-x\times2e^{2x}}{{(e^{2x})}^{2}}

Simplified

y' = \frac{e^{2x}-2xe^{2x}}{{e^{4x}}}


Substituted (1, 1/e^2 )

y = \frac{e^{2(1)}-2(1)e^{2(1)}}{{e^{4(1)}}}


Simplified

y = \frac{e^{2}-2e^{2}}{{e^{4}}}

Take out  e^{2}

y = -\frac{1}{{e^{2}}}