Question 894150
The gradient is the derivative of the function.
In this case,
{{{z=2e^(4t)}}}
{{{dz/dt=2e^(4t)*4}}}
{{{dz/dt=8e^4t}}}
The value of the tangent line to the function at any point is the value of the derivative at that point. 
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As an example, when {{{t=0}}},{{{z=2}}},{{{dz/dt=8}}}
So the equation of the tangent line is,
{{{z-2=8(t-0)}}}
{{{z=8t+2}}}
On the graph, {{{x=t}}} and {{{y=z}}}
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{{{graph(300,300,-2,2,-1,5,2e^(4x),8x+2)}}}