Question

If g(x)= logx3, then g'(x)=?​

Answer 1

To find the derivative of the function g(x) = log(x^3), we can use the chain rule of differentiation:

g'(x) = d/dx [log(x^3)]
= 1/(x^3) * d/dx [x^3] (chain rule: d/dx [log(u)] = 1/u * d/dx [u])
= 1/(x^3) * 3x (power rule: d/dx [x^n] = n*x^(n-1))

Simplifying this expression, we get:

g'(x) = 3/x^2

Therefore, the derivative of g(x) = log(x^3) is g'(x) = 3/x^2.