High School

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Find the derivative of the function:

\[ y = 9x^5 - 5x^3 + 4x - 10 \]

What is \( y' \)?

A. \( 45x^4 - 15x^2 + 4 \)
B. \( 45x^4 - 15x^2 + 4x \)
C. \( 45x^4 - 15x^2 + 4x - 10 \)
D. \( 45x^4 - 15x^2 + 4x + 10 \)

Answer :

Final answer:

The derivative of the function y = 9x⁵ - 5x³ + 4x - 10 is 45x⁴ - 15x² + 4. Hence, option A is the correct answer.

Explanation:

Derivatives are defined as the varying rate of change of a function with respect to an independent variable. The derivative is primarily used when there is some varying quantity, and the rate of change is not constant. The derivative is used to measure the sensitivity of one variable (dependent variable) with respect to another variable (independent variable).

The derivative of the function y=9x⁵-5x³+4x-10 is found by applying the power rule to each term, resulting in a derivative of y'=45x⁴-15x²+4.The question asks to find the derivative of the function y=9x⁵-5x³+4x-10. To find the derivative, we apply the power rule: d/dx(x⁵) = 5x⁴, d/dx(x³) = 3x², and d/dx(x) = 1. Constants have a derivative of 0.

Applying these rules to each term in the function gives us:

  • The derivative of 9x⁵ is 45x⁴.
  • The derivative of -5x³ is -15x².
  • The derivative of 4x is 4.
  • The derivative of the constant -10 is 0.

Combining these results, the derivative y' is 45x⁴-15x²+4.

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