To find the derivative of a function and evaluate it at a specific value, we will use the power rule for differentiation.
Given that F(x) = (2x^5 - 6x^3 + 7x^2 + 100)^4, the derivative F'(x) can be found using the chain rule and the power rule.
F'(x) = 4(2x^5 - 6x^3 + 7x^2 + 100)^3(10x^4 - 18x^2 + 14)
Next, we evaluate the derivative at x = 1:
F'(1) = 4(2(1)^5 - 6(1)^3 + 7(1)^2 + 100)^3(10(1)^4 - 18(1)^2 + 14)= 4(2 - 6 + 7 + 100)^3(10 - 18 + 14)= 4(103)^3(-4)= 4(106291)^3(-4)= 4(-1441396713)(-4)= 22836747408
Therefore, F'(1) = 22836747408.
To find the derivative of a function and evaluate it at a specific value, we will use the power rule for differentiation.
Given that F(x) = (2x^5 - 6x^3 + 7x^2 + 100)^4, the derivative F'(x) can be found using the chain rule and the power rule.
F'(x) = 4(2x^5 - 6x^3 + 7x^2 + 100)^3(10x^4 - 18x^2 + 14)
Next, we evaluate the derivative at x = 1:
F'(1) = 4(2(1)^5 - 6(1)^3 + 7(1)^2 + 100)^3(10(1)^4 - 18(1)^2 + 14)
= 4(2 - 6 + 7 + 100)^3(10 - 18 + 14)
= 4(103)^3(-4)
= 4(106291)^3(-4)
= 4(-1441396713)(-4)
= 22836747408
Therefore, F'(1) = 22836747408.