Question

What is the derivative of (x²)/2?"
a) x
b) 2x
c) 1/x
d) x²

Answer 1

The derivative of (x²)/2 is x, which is found using the power rule for differentiation where the exponent is multiplied by the coefficient and then the exponent is decreased by one.

Step-by-step explanation:

The derivative of (x²)/2 is found by using the power rule for differentiation. The power rule states that if f(x) = xn, then f'(x) = nxn-1. Applying the power rule to our function:

• Let f(x) = (x²)/2.
• Multiplying the exponent by the coefficient, we get f'(x) = (2*x(2-1))/2.
• Simplifying, we find that f'(x) = x.

Therefore, the derivative of (x²)/2 is simply x, which corresponds to option (a).