What is the derivative of 6/x?
Explain how you got the answer please.
6/x is 6*x^-1
d/dx(x^n) = n*x^(n-1)
d/dx(6*x^-1) = 6*(-1)*x^-2
= -6/x^2
To find the derivative of the function 6/x, we can use the power rule for derivatives. The power rule states that if we have a function f(x) = x^n, then its derivative is given by f'(x) = nx^(n-1).
In this case, we can rewrite the function 6/x as 6x^(-1), where n = -1. Applying the power rule, we differentiate each term separately:
f'(x) = -1 * 6x^(-1-1) = -6x^(-2)
This simplifies to f'(x) = -6/x^2.
So, the derivative of 6/x is -6/x^2.