Differentiate the Given function. Simplify the Answer and show solution:

Question

18.) f(x) = 1/4 x^8 - 1/2 x^6 - x +2

and

20.) f(u) = 0.07u^4 - 1.21u^3 +3u - 5.2

 

210) f(x) = (x+1/x)^2

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Answer 1

Hi Krissela,

 

18.) f(x) = 1/4 x^8 - 1/2 x^6 - x +2

 

 

To differentiate f(x) you can use the power rule.

 

            f '(x) = 8(1/4)x^(8-1) -6(1/2)x^(6-1)- 1x^(1-1)

            f '(x) = 2x^7 - 3x^5 -1

 

Note:  x^0= 1 and the derivative of a constant is zero.
20.) f(u) = 0.07u^4 - 1.21u^3 +3u - 5.2

 

The same process for this problem.

         

            f '(u) = 4(0.07)u^(4-1) - 3(1.21)u^(3-1) +3

            f '(u) = .28u^3 - 3.63u^2 +3

21) f(x) = (x+1/x)^2

 

 

For this problem the Chain Rule can be used.

 

 

                                  f '(x)=2 (x +1/x)^(2-1)*d/dx(x+1/x)

 

                                  f '(x)=2 (x +1/x)^(1)*d/dx(x+1/x)

                                  f '(x)=2 (x +1/x)*d/dx(x+1/x)

                                

Note: 1/x can be written as  1x^-1   then the derivative would be  (-1)1x^(-1-1) which simplifies to   -x^(-2).

-x^(-2) can be written as   -1/x^2

 

 

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

Hope this shows you how the process is done.

THINK MATH!