Question

find the derivative of y with respect to x.
y = log₆x + log₆x⁶
dy/dx = □

Explanation:

Step1: Simplify the second - log term

Use the power - rule of logarithms $\log_aM^n=n\log_aM$. So, $\log_6x^6 = 6\log_6x$. Then $y=\log_6x + 6\log_6x=7\log_6x$.

Step2: Recall the derivative formula for $\log_ax$

The derivative of $\log_ax$ with respect to $x$ is $\frac{1}{x\ln a}$. Here $a = 6$, so the derivative of $y = 7\log_6x$ with respect to $x$ is $y^\prime=7\times\frac{1}{x\ln 6}$.

Answer:

$\frac{7}{x\ln 6}$