Find the derivative of the following function.𝑦=2(𝑥3−5𝑥2−3𝑥)35

To find the derivative of the function y = 2(x^3 - 5x^2 - 3x)^35, we will use the chain rule. The chain rule states that the derivative of a composite function is the derivative of the outer function times the derivative of the inner function.

Step 1: Identify the outer and inner functions. In this case, the outer function is f(u) = 2u^35 and the inner function is g(x) = x^3 - 5x^2 - 3x.

Step 2: Find the derivative of the outer function. The derivative of f(u) = 2u^35 is f'(u) = 70u^34.

Step 3: Find the derivative of the inner function. The derivative of g(x) = x^3 - 5x^2 - 3x is g'(x) = 3x^2 - 10x - 3.

Step 4: Apply the chain rule. The chain rule states that (f(g(x)))' = f'(g(x)) * g'(x). So, the derivative of y = 2(x^3 - 5x^2 - 3x)^35 is y' = f'(g(x)) * g'(x) = 70(g(x))^34 * g'(x) = 70(x^3