1. ## Quicky question about using the Chain Rule

I am curious as to how you would write the derivative when using the chain rule for longer polynomials?

we learned how to do examples such as y = (5x + 1)^4

but I am stumped as to how you would write it when the example is per se,
y = 2(2x + 4(3x + 2)^5 - 5x^2)^4 - 6x

so for this example, i would get

y' = 8(2x + 4(3x + 2)^5 - 5x^2)^3 x (the derivative of the stuff inside the bracket "u") - 6

What i'm wondering is, for the "u" part, how do i write it?

would I go 2 + 20(3x+2)^4 x 3 - 10x or would i write it such as 2(20(3x+2)^4)(3)(10x) and multiply them all together like that

2. Originally Posted by mneox
I am curious as to how you would write the derivative when using the chain rule for longer polynomials?

we learned how to do examples such as y = (5x + 1)^4

but I am stumped as to how you would write it when the example is per se,
y = 2(2x + 4(3x + 2)^5 - 5x^2)^4 - 6x

so for this example, i would get

y' = 8(2x + 4(3x + 2)^5 - 5x^2)^3 x (the derivative of the stuff inside the bracket "u") - 6

What i'm wondering is, for the "u" part, how do i write it?

would I go 2 + 20(3x+2)^4 x 3 - 10x or would i write it such as 2(20(3x+2)^4)(3)(10x) and multiply them all together like that

It is like the first thing you said, $(2+20(3x+2)^4(3)-10x)$ When using chain rule you multiply the first part by the second while still following all the other rules of differentiation.
Your answer should look like: $8(2x+4(3x+2)^5-5x^2)^3(2+60(3x+2)^4-10x)-6$ You should multiply the 8 through the second part as well there to polish it off.