Find the derivative of f(x) = 4x^3 - 5x^2 + 7x - 9.

Step 1: Differentiate each term separately.

The function is:
f(x) = 4x^3 - 5x^2 + 7x - 9

Use the power rule:
d/dx(x^n) = nx^(n-1)

Step 2: Differentiate 4x^3.

d/dx(4x^3) = 4(3x^2) = 12x^2

Step 3: Differentiate -5x^2.

d/dx(-5x^2) = -5(2x) = -10x

Step 4: Differentiate 7x and -9.

d/dx(7x) = 7

d/dx(-9) = 0

Step 5: Combine the derivatives.

f'(x) = 12x^2 - 10x + 7

Therefore, the derivative is 12x^2 - 10x + 7.