Question

Find the derivative of the function.
f(x) = (2x − 5)^4(x2 + x + 1)^5

....the answer that I got was:
f(x) = 20(2x-5)^3(2x)(x^2+x+1)^4(2x+1)

Answer 1

Did you use product rule?

Answer 2

I did but I think I went horribly wrong some where

Answer 3

I can show you what i did

Answer 4

Do you need the answer in any particular form? (fully simplified, fully factored, etc.)

Answer 5

Fully simplified I'm guessing.

Answer 6

hrm, that'll get annoying to fully expand that 5th power of a quadratic trinomial, but let's just get something correct for a derivative first..
What were your first 2 steps?

Answer 7

f(x) = (2x − 5)4(x2 + x + 1)5
=4(2x-5)^3(2x)5(x^2+x+1)^4(2x+1)
=4*5(2x-5)^3(2x)(x^2+x+1)^4(2x+1)
=20(2x-5)^3(2x)(x^2+x+1)^4(2x+1)

Answer 8

You're not adding the products correctly, and the derivative of 2x-5 is 2 not 2x.

Answer 9

product rule is "first times the derivative of the second plus second times the derivative of the first."

Answer 10

completely missed the 2x

so the formula if like this?
f'(x)g(x)+f(x)g'(x)

Answer 11

Yes.
\[Let \;s(x)=(2x-5)^4; \;t(x)=(x^2+x+1)^5. \]
\[s'(x)=(2)(2x-5)^3; \; t'(x)=(5)(2x+1)(x^2+x+1)^4. \]
\[\frac{d}{dx}s(x)t(x)=s(x)t'(x)+s'(x)t(x).\]

Answer 12

Oops, forgot the (4) in the s'(x) there.

Answer 13

Should read: \[s'(x)=(4)(2)(2x-5)^3\]

Answer 14

That's the answer?
really?

Answer 15

It's the bits and pieces of the answer - you still need to put them all together and simplify.

Answer 16

Remember that I took your f(x) and expressed it as f(x)=s(x)t(x) to showcase the product rule. s'(x) =/= f'(x).

Answer 17

Now what do you have? (I recommend against trying to simplify it all the way down. )