Final answer:
To find the derivative of the given function, we can use the product rule. After applying the product rule and simplifying the expression, we get the derivative as 10x^9.
Step-by-step explanation:
In calculus, the derivative measures how a function changes as its input (independent variable) changes. It provides the rate at which a quantity is changing at any given point. Geometrically, the derivative represents the slope of the tangent line to the graph of a function at a specific point.
To find the derivative of the product of two functions using the product rule, we use the formula:
(f(x) * g(x))' = f'(x) * g(x) + f(x) * g'(x)
For the given function y = x^6 * x^4, we can apply the product rule:
y' = (6x^5 * x^4) + (x^6 * 4x^3)
Simplifying further, we get:
y' = 6x^9 + 4x^9 = 10x^9