Find the derivative of the function y=(3+e^x+8x^3)^2*(2x+e^2x)

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We have to find the derivative of y=(3+e^x+8x^3)^2*(2x+e^2x)

We can use the product rule here

y=(3+e^x+8x^3)^2*(2x+e^2x)

y' = [(3+e^x+8x^3)^2*(2x+e^2x)]'

=>y' = [(3+e^x+8x^3)^2]*(2x+e^2x)]' + [(3+e^x+8x^3)^2]' *(2x+e^2x)]

=> y' = [(3+e^x+8x^3)^2]*(2+2e^2x) + [2*(3+e^x+8x^3)* (e^x+24x^2] *(2x+e^2x)

We get the derivative as: [(3+e^x+8x^3)^2]*(2+2e^2x) + [2*(3+e^x+8x^3)* (e^x+24x^2] *(2x+e^2x)

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