Question

Find all the derivatives of the function defined by f(x)=2x^(4)-5x^(3)+3x^(2)-x-100

Answer 1

To find the derivatives of the function f(x) = 2x^4 - 5x^3 + 3x^2 - x - 100, you can use the power rule.

Step-by-step explanation:

To find the derivatives of the function f(x) = 2x^4 - 5x^3 + 3x^2 - x - 100:

1. Take the derivative of each term separately using the power rule.
2. The power rule states that the derivative of x^n is nx^(n-1).
3. Apply the power rule to each term and simplify the result.
4. The derivatives of the function f(x) are:

• f'(x) = 8x^3 - 15x^2 + 6x - 1
• f''(x) = 24x^2 - 30x + 6
• f'''(x) = 48x - 30
• f''''(x) = 48