High School

Find the derivative of the following with respect to [tex]\pi x \pi[/tex]:

[tex]f(x) = 5x^7 - 12x^5 + 4x^3 - 12x^2 - x + 17[/tex]

a) [tex]\pi f'(x) = 35x^6 - 60x^4 + 12x^2 - 24x - 1 \pi[/tex]

b) [tex]\pi f'(x) = 35x^6 - 60x^4 + 12x^2 - 12x - 1 \pi[/tex]

c) [tex]\pi f'(x) = 35x^6 - 60x^4 + 12x^2 - 24x \pi[/tex]

d) [tex]\pi f'(x) = 35x^6 - 60x^4 + 12x^2 - 12x \pi[/tex]

Answer :

Final answer:

The derivative of the given function is found by applying the power rule to each term. The correct derivative with respect to (x) (x) is option b) (f'(x) = 35x^6 - 60x^4 + 12x^2 - 24x - 1

Explanation:

To find the derivative of the function f(x) = 5x7 - 12x5 + 4x3 - 12x2 - x + 17 with respect to (x) (x), we will apply the power rule to each term individually. The derivative of a term like axn is anxn-1. After calculating the derivatives for each term, the result is given by:

  1. f'(x) = 35x6 (derivative of 5x7)
  2. - 60x4 (derivative of -12x5)
  3. + 12x2 (derivative of 4x3)
  4. - 24x (derivative of -12x2)
  5. - 1 (derivative of -x)

The constants in the function do not affect the derivative as their derivative is zero. Hence, the correct answer is b)
f'(x) = 35x6 - 60x4 + 12x2 - 24x - 1

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