Need Derivative help with finding f' for f(x) = 4x(5+2x)^9

[calphobe^2]

Please help me step this derivative using product/chain rule:

f(x) = 4x(5+2x)^9

f ' (x) =?

I'm trying to get to: 20(5+2x)^8(1+4x)

 

[galactus]

\(\displaystyle \L\\4x(5+2x)^{9}\)

Product rule:

\(\displaystyle \L\\4x(9)(5+2x)^{8}(2)+(5+2x)^{9}(4)\)

Simplify:

\(\displaystyle \L\\72x(5+2x)^{8}+4(5+2x)^{9}\)

Now, factor out \(\displaystyle (5+2x)^{8}\), then factor out 20.

 

[calphobe^2]

Sorry, I did get that far. Will you show me how? Next time I'll post to the algebra forum. Thanks.

 

[galactus]

No, that's OK. This is calculus, It's just the hardest part of calc is the algebra.



Starting where we left off. A sI said, factor out \(\displaystyle (5+2x)^{8}\)

\(\displaystyle \L\\(5+2x)^{8}(72x+4(5+2x))\)...[1]

\(\displaystyle \L\\(5+2x)^{8}(80x+20)\)

Factor out 20:

\(\displaystyle \L\\20(5+2x)^{8}(4x+1)\)

There.

If you got as far as [1], you didn't have much to go.

 

[calphobe^2]

Thanks for the help. I hope to repay the favor someday.