Question

Derivative of `log_6`x with respect 6^x to is ______

Options

• `1/(x 6^x)`

• `1/(6^x (log6)^2)`

• `1/(x 6^x (log 6)^2)`

• `1/(x(log6)^2)`

Answer 1

Derivative of `log_6`x with respect 6^x to is `underline(1/(x 6^x (log 6)^2)).`

Explanation:

Let `y = log_6x` and `z = 6^x`

∴ `dy/dx = 1/(x log6)` and `dz/dx = 6^x log6`

∴ `dy/dz = (dy/dx)/(dz/dx) = (1/(xlog6))/(6^x log6) = 1/(x 6^x(log 6)^2)`