Final answer:
The derivative of the function y = 17x² + 3x³ - 5x is found by applying the power rule to each term, resulting in y' = 34x + 9x² - 5.
"The correct option is approximately option A"
Step-by-step explanation:
Finding the Derivative
To find the derivative of the function y = 17x² + 3x³ - 5x, we will apply the power rule for differentiation. The power rule states that if y = ax^n, then the derivative, denoted as y' or dy/dx, is y' = n·ax^(n-1). Let's apply this rule to each term in the function:
- For the term 17x², the derivative is 2·17x = 34x.
- For the term 3x³, the derivative is 3·3x^(3-1) = 9x².
- For the term -5x, the derivative is simply -5, since the derivative of x with respect to x is 1.
Combining these, we get the derivative of the function: y' = 34x + 9x² - 5. So the correct answer is A) y' = 34x + 9x² - 5.