1. Identify the function as a product of two separate functions, namely u = (2x^4 + 1) and v = tan(x).
2. Apply the product rule for differentiation, which states that the derivative of the product of two functions is the derivative of the first function times the second function plus the first function times the derivative of the second function. In mathematical notation, this is written as (uv)' = u'v + uv'.
3. Differentiate u = (2x^4 + 1) with respect to x to get u' = 8x^3.
4. Differentiate v = tan(x) with respect to x to get v' = sec^2(x).
5. Substitute u, u', v, and v' into the product rule to get the derivative of y = (2x^4 + 1)tan(x), which is y' = u'v + uv' = 8x^3tan(x) + (2x^4 + 1)sec^2(x).

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1. Identify the function as a product of two separate functions, namely u = (2x^4 + 1) and v = tan(x).
2. Apply the product rule for differentiation, which states that the derivative of the product of two functions is the derivative of the first function times the second function plus the first function times the derivative of the second function. In mathematical notation, this is written as (uv)' = u'v + uv'.
3. Differentiate u = (2x^4 + 1) with respect to x to get u' = 8x^3.
4. Differentiate v = tan(x) with respect to x to get v' = sec^2(x).
5. Substitute u, u', v, and v' into the product rule to get the derivative of y = (2x^4 + 1)tan(x), which is y' = u'v + uv' = 8x^3tan(x) + (2x^4 + 1)sec^2(x).

To obtain the derivative of y = (2x4 + 1)tan xWe utilize the following steps. Arrange the order to obtain the solution.

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