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Moved from a technical math section, so missing the template

So i have an equation problem that i need to find the 2nd derivative of, but my understanding of the chain rule is not the best. I tried working it out but i dont know if i did it correctly.

i was given the equation y=4(x

So to take the first derivative, i started off by using the chain rule as i understand it and simplified it to:

y'=[12(x

This is where i start to get confused. I dont really know for certain how im supposed to take the 2nd derivative of that. I assumed that i needed to actually multiply and simplify the first derivative to take the 2nd, but i dont know if what i did or what i got was correct.

I simplified the first derivative and ended up with: y'=24x

Then i calculated the 2nd derivative and got: y''=120x

Would this be correct?

i was given the equation y=4(x

^{2}+5x)^{3}So to take the first derivative, i started off by using the chain rule as i understand it and simplified it to:

y'=[12(x

^{2}+5x)^{2}][2x+5]This is where i start to get confused. I dont really know for certain how im supposed to take the 2nd derivative of that. I assumed that i needed to actually multiply and simplify the first derivative to take the 2nd, but i dont know if what i did or what i got was correct.

I simplified the first derivative and ended up with: y'=24x

^{5}+60x^{4}+1200x^{3}+3000x^{2}Then i calculated the 2nd derivative and got: y''=120x

^{4}+240x^{3}+3600x^{2}+6000xWould this be correct?