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

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

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

##### 1 Answer

Jan 29, 2018

#### 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

*Final Answer*