Question

Find the derivative of e^(2x) * (x^5 + 4^x).

I got:
e^(2x)(x^5 + 4^x) + e^(2x)(5x^4 + 4^x * ln(4))
using the product rule and exponent rule(s), but this is wrong. Any idea where I'm going wrong?

Answer 1

You are using the product rule incorrectly.

The product rule says that the derivative of f(x) times g(x) is

f(x) g ' (x) + g(x) f ' (x)

Answer 2

f(x) = e^(2x), so f ' (x) = 2e^(2x)
g(x) = (x^5 + 4^x), so g ' (x) = 5x^4 + (ln 4)(4^x)

Answer 3

Thanks! Can't believe I missed the 2.

Answer 4

Now, you can find the derivative of (e^(2x)) (x^5 + 4^x)

Answer 5

It's more than that...you started off with f(x) g(x) and it should be f(x) g ' (x)

Answer 6

Besides missing the 2, I believe you did not use the product rukle correctly.

Answer 7

rule*

Answer 8

How? All I missed was the 2 before the first e^(2x), unless I copied it over wrong I was right (I just checked, I now have the correct response according to the online homework thing I use).

Answer 9

oh...ok