Can you help me with the Product Rule?

The question I’m stuck on is as follows:

f(x) = x^2(1 + 4e^x)

I don’t know where to start. Any ideas?

Top 1 Answers

A few days ago

Anonymous

Favorite Answer

I assume the (1 + 4e^x) is not in the exponent or you wouldn’t be asking about the product rule.

Remember the product rule. For f and g, both functions of x:

d/dx (fg) = f’g + fg’

In this case, f(x) = x^2 and g(x) = 1 + 4e^x

f’ = 2x, g’ = 4e^x

So:

derivative = f’g + fg’ = 2x(1 + 4e^x) + (x^2)(4e^x)

which you are free to simplify as you choose.

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