Find the derivative of the function.F (x) = (5x6 + 2x3)4

To find the derivative of the function F(x) = (5x^6 + 2x^3)^4, 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 u^4 and the inner function is 5x^6 + 2x^3.

Step 2: Find the derivative of the outer function. The derivative of u^4 with respect to u is 4u^3.

Step 3: Find the derivative of the inner function. The derivative of 5x^6 + 2x^3 with respect to x is 30x^5 + 6x^2.

Step 4: Apply 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. So, the derivative of F(x) is 4*(5x^6 + 2x^3)^3 * (30x^5 + 6x^2).

So, F'(x) = 4*(5x^6 + 2x^3)^3 * (30x^5 + 6x^2).