Final answer:
The derivative of y=2x³-13x²+35x+7 is found using the power rule of differentiation, resulting in dy/dx = 6x² - 26x + 35.
Step-by-step explanation:
Differentiate the Function
The question asks to find the derivative of the function y=2x³-13x²+35x+7. Differentiation is a fundamental concept in calculus that deals with finding the rate at which a function is changing at any given point. To differentiate this polynomial function, we can apply the power rule of differentiation, which states that if y=x^n, then dy/dx=n*x^(n-1). Using this rule, the derivative of each term of the polynomial is calculated as follows:
The derivative of 2x³ is 6x².
The derivative of -13x² is -26x.
The derivative of 35x is +35.
The derivative of the constant 7 is 0, as constants have a derivative of zero.
Combining these, the derivative dy/dx = 6x² - 26x + 35.