Question

Find the derivatives of y = (x2 + 1)(x3 + 3)​

Answer 1

Answer:

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Using the product Rule with u = x2 + 1 and v = x3 + 3, we find

d / (dx) [(x2 + 1)(x3 + 3)] = (x2 + 1)(3x2) + (x3 + 3)(2x)

= 3x4 + 3x2 + 2x4 + 6x = 5x4 + 3x2 + 6x

Example can be done as well (perhaps better) by multiplying out the original expression for y and

differentiating the resulting polynomial. We now check:

y = (x2 + 1)(x3 + 3) = x5 + x3 + 3x2 + 3

dy / dx = 5x4 + 3x2 + 6x

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