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Find the derivative of function. `y=x(6^(-2x))`

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jesuhlocun103 | Student, College Freshman | eNoter

Posted February 21, 2013 at 8:11 PM via web

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Find the derivative of function.

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

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mjripalda | High School Teacher | (Level 3) Educator

Posted February 21, 2013 at 11:10 PM (Answer #1)

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`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` .

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