Given, f(x) = 4/x
We have to find the derivative of it.
First we have to use property of negative exponents. We know that, 1/a = a⁻¹.
So here, f(x) = 4/x = 4x⁻¹
f'(x) = 4×(-1)×(x)⁽⁻¹⁻¹⁾
= 4×(-1)×(x)⁻²
= (-4)(x)⁻²
= -4/x²
So we have got derivative of f(x) which is f'(x) = -4/x²
Now we have to find the derivative at x = 2. To find the value at x =2, we have to plug in 2 in the place of x.
f'(2) = -4/(2)² = -4/4 = -1
We have got the required answer derivative of f(x) at x =2 is -1
So option B is correct.
