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At the x-intercepts of the graph, the line crosses the x-axis. This means that the y-value at these points equals 0. We must therefore make x^2+2x equal to 0 and simplify the equation. x^2+2x = 0 is the s...

y=e^(x)*sin(x)   

Use the product rule:   y'=uv'+vu'    y=u*v          

Differentiate: u=e^(x)   u'=e^(x)    v=sin(x)  v'=cos(x)

Sub into the product rule: y'=e^(x)*cos(x)+e^(x)*sin(x...