Find f ?(x) for problems 1-5, and write your final answer on the line in the for

Question

Find f ?(x) for problems 1-5, and write your final answer on the line in the form indicated. All answers must be simplified (i.e. like terms combined/cancelled if applicable). SHOW ALL WORK!! Turn in one sheet for yourself, or if you worked with a partner, one sheet for the two of you. (2 ea.) 1. f(x) = 6x^4 + 15x^3 ? 3x^2 + 7 (factored form) 2. f(x) = (2x + 5)^2(x + 1)^2 (factored form)3. F(x) = 2 + x^2 /3x^2-x (1 fraction, numerator simplified) 4. f(x) = ln x-3/x 5. f(x) = squareroot (1+x) (one fraction, pos. exponents)

Explanation / Answer

f(x)=6x4+15x3-3x2+7
f'(x)=24x3+45x2-6x =3x(8x2+15x-2)

f(x)=(2x+5)3(x+1)2
f'(x)=(2x+5)3 * 2(x+1)+(x+1)2 *3(2x+5)2 *2
   =2*(2x+5)2 (x+1) [(2x+5)+(x+1)3]
   =2*(2x+5)2 (x+1)[2x+5+3x+3]
   ==2*(2x+5)2 (x+1) [5x+8]

f(x)=(2+x2)/(3x2-x)
f'(x)=[(3x2-x)*2x-(2+x2)*(6x-1)]/(3x2-x)2
   =[6x3-2x2-(12x+6x3-2-x2)]/(3x2-x)2
   =[6x3-2x2-12x-6x3+2+x2]/(3x2-x)2
   =(-x2-12x+2)/(3x2-x)2


f(x)=ln(x)-(3/x)
f'(x)=(1/x)+(3/x2)
   = (1/x) [1+(3/x)]

f(x)=(1+x1/2)1/2
f'(x)= (1/2) (1+x1/2)-1/2 *(1/2)x-1/2
   =(1/4) x-1/2 (1+x1/2)-1/2

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