High School

Find the derivative of the function:

\[ y = 17x^{-2} - 16x^3 - 4x \]

Choose the correct derivative:

A. \(-34x^{-1} + 48x^2\)

B. \(-34x^{-3} + 48x^2 - 4\)

C. \(-34x^{-3} + 48x^2\)

D. \(-34x^{-1} + 48x^2 - 4\)

Answer :

Final answer:

The derivative of the function y = 17x⁻² - 16x³ - 4x is -34x⁻³ + 48x² - 4, derived by applying the power rule to each term individually. Therefore, the correct answer is option b) -34x⁻³+48x²-4 .

Explanation:

The student asked to find the derivative of the function y = 17x⁻² - 16x³ - 4x. To find the derivative, we use the power rule, which states that the derivative of x to the power of n, denoted as x^n, is n times x to the power of n-1. Applying this rule to each term in the function we get:

  • The derivative of 17x⁻² is -34x⁻³.
  • The derivative of -16x³ is -48x².
  • The derivative of -4x is -4.

Therefore, the derivative of the given function is -34x⁻³ + 48x² - 4.

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