Question

What is the derivative of f(x) = (x)(6^-2x)?

I got 6^-2x - 2x(ln6). Is this correct?

Answer 1

`6^(-2x)(1-2xln6)`

Explanation:

First, remember that:

`d/dx(a^x) = d/dx(e^(xlna)) = e^(xlna) * lna = a^x lna`

So, using product rule, we can differentiate the expression as:

`d/dx (x * 6^(-2x)) = d/dx(x) * 6^(-2x) + x * d/dx6^(-2x)`

`= 6^(-2x) + x * (6^color(blue)(-2x) * ln6 * d/dx(color(blue)(-2x)))`

`= 6^(-2x) -2xln6(6^(-2x))`

`= 6^(-2x)(1-2xln6)`

Your answer was very close to correct; you just forgot the `6^(-2x)` in the second term. Hope this helps!

Final Answer