Final answer:
To differentiate the function y=(3x²-1)(5x-2)², you can use the product rule. The product rule states that if we have two functions, u(x) and v(x), the derivative of their product is given by (u(x)v(x))' = u'(x)v(x) + u(x)v'(x). Applying the product rule and simplifying, we find y' = 6x(5x-2)² + 10(3x²-1)(5x-2).
Step-by-step explanation:
To differentiate the function y = (3x²-1)(5x-2)², we can use the product rule. The product rule states that if we have two functions, u(x) and v(x), then the derivative of their product is given by:
(u(x)v(x))' = u'(x)v(x) + u(x)v'(x)
Applying the product rule to the given function, we have:
y' = (3x²-1)'(5x-2)² + (3x²-1)(5x-2)²'
Now, we just need to find the derivatives of each term using the power rule and the chain rule:
y' = (6x)(5x-2)² + (3x²-1)(2)(5x-2)(5)
Simplifying further, we get:
y' = 6x(5x-2)² + 10(3x²-1)(5x-2)