Question

Obtain the derivative of the following function using the addition and subtraction rule:

F(x) = 5x10 - 2x2 + x - 1

Answer 1

Explanation:

To obtain the derivative of F(x) = 5x^10 - 2x^2 + x - 1 using the addition and subtraction rule, we can take the derivative of each term separately and then add or subtract the resulting derivatives.

The derivative of 5x^10 is:

(5x^10)' = 50x^9

The derivative of -2x^2 is:

(-2x^2)' = -4x

The derivative of x is:

(x)' = 1

The derivative of -1 is:

(-1)' = 0

Putting these derivatives together using the addition and subtraction rule, we get:

F'(x) = (50x^9) - (4x) + (1) + (0)

Simplifying this expression, we get:

F'(x) = 50x^9 - 4x + 1

Therefore, the derivative of F(x) = 5x^10 - 2x^2 + x - 1 using the addition and subtraction rule is F'(x) = 50x^9 - 4x + 1.