Find the derivative of function.

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

Expert Answers

An illustration of the letter 'A' in a speech bubbles

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

`y=x(36^(-x))`

To take the derivative of  y, apply product rule which is `(u*v)=v*u'+u*v'` .

So let,

`u=x`          and          `v=36^(-x)`

Then, take the derivative of u and v.

`u'=1`

To get v', apply the derivative of exponential functions which is `(a^u)=a^u*lna*u'` .

`v'=36^(-x)*ln36*(-x)'`

`v'=36^(-x)*ln36*-1`

`v'=-36^(-x)ln36`

And, plug-in u , v, u' and v' to the formula of product rule.

`y'=36^(-x)*1+ (-36^(-x)ln36)`

`y'=36^(-x)-36^(-x)ln36`

Express 36 with positive exponent.

`y'=1/36^x-(ln36)/36^x`

Hence, the derivative of the given function is `y'=1/36^x-(ln36)/36^x` .

See eNotes Ad-Free

Start your 48-hour free trial to get access to more than 30,000 additional guides and more than 350,000 Homework Help questions answered by our experts.

Get 48 Hours Free Access
Approved by eNotes Editorial