Chain Rule/Derivatives HW

What did I do wrong?
1. Find f'(x) when f(x)= 5x(sinx + cosx)
My answer: cos(4x^2)- sin(6x^2)/(5x^2)
2. Find f'(x) when f(x)= ((x^3) + 4x + 4))^2
My answer: 6x^2(x^3 + 4x + 4)
3. Find f'(x) when f(x)= (3x + 8)^-3
My answer: -6(3x + 8)
4. Find f'(x) when f(x)= Sq root of (5x + 8)
My answer: x/5x + 8
5. Find f'(x) when f(x)= cos(3x + 2)
My answer: ?
6. Find f'(x) when f(x)= sin(cos(x^5))
My answer: ?

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1. Find f'(x) when f(x)= 5x(sinx + cosx)
My answer: cos(4x^2)- sin(6x^2)/(5x^2)

Use the formula ( g(x) h(x))'=g'(x)h(x)+g(x)h'(x)

f'(x)= 5(sinx + cosx) +5x( cosx-sinx) =(5-5x)sinx+(5+5x)cosx=5(1-x)sinx+5(1+x)cosx.

So your answer is not correct.

2. Find f'(x) when f(x)= ((x^3) + 4x + 4))^2
My answer: 6x^2(x^3 + 4x + 4)

The chain-rule is

(f g)'(x)=f '(g(x)) g'(x)

For this problem g(x)= (x^3) + 4x + 4 Thus

f(x)=(f g)(x)=g^2 (x). ...