Question

F(x)=(7x^3-2x/4x+5)'

Answer 1

7x^2
производная от 5-ти равна нулю, производная от дроби равна 0, так как по правилу раскрываешь и будет (8х-8х)/16х^2=0/16х2=0

Answer 2

To differentiate F(x), we will need to use the quotient rule and the power rule of differentiation.

The quotient rule states that for functions u(x) and v(x),

d/dx(u(x)/v(x)) = (v(x)*du/dx - u(x)*dv/dx)/(v(x))^2

And the power rule states that for a function f(x) = x^n,

d/dx(f(x)) = n*x^(n-1)

Using these rules, we can differentiate F(x) as follows:

F(x) = (7x^3 - 2x)/(4x + 5)

F'(x) = [((4x + 5)*d/dx(7x^3 - 2x)) - (7x^3 - 2x)*d/dx(4x + 5)] / (4x + 5)^2 (Applying the quotient rule)

F'(x) = [(4x + 5)*(21x^2 - 2) - (7x^3 - 2x)*4] / (4x + 5)^2 (Using the power rule to differentiate 7x^3 - 2x and 4x + 5)

F'(x) = [84x^3 + 97x^2 - 20x - 20] / (4x + 5)^2

Therefore, the derivative of F(x) is (84x^3 + 97x^2 - 20x - 20) / (4x + 5)^2.