Hi this is confusing me

Question

Use the product rule to find the derivative of

(2x^6-4x^10)(4e^x+9)

You do not need to expand out your answer.

Answer 1

See the video.

Answer 2

Hi Morgen!

If you're given two functions multiplied by each other, you'll want to use the product rule to find the derivative of that product:

Let f(x) = 2x⁶-4x¹⁰, f'(x) = 12x⁵-40x⁹, g(x) = 4e^x+9, and g'(x) = 4e^x

Product rule states that d/dx f(x)g(x) = f'(x)g(x) + f(x)g'(x)

Therefore, d/dx (2x^6-4x^10)(4e^x+9) = (12x⁵-40x⁹)(4e^x+9) + (2x⁶-4x¹⁰)(4e^x)

Hope this helped!