Question

Find the derivatives of the following functions using the differentiation rules.

f(x)=(x^3-2x^2+x+1)(sqrt(x)-3x+9)

I did:

f'(x)=[x^3-2x^2+x+1][(1/2x^(-1/2)-3]+[x^(1/2)-3x+9][3x^2-4x+1]

which I got to be

[-12x^3+(7/2)x^(5/2)+46x^2-5x^(3/2)-42x+(3/2)x^(1/2)+6]/[2x^(1/2)]

I just wanted to make sure I didn't make any mistakes because the fractions are confusing.
Your first line derivative is correct, however, I haven't got a clue how you got that last line.
Thats what I got whenever I simplified it

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