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

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lemjay | High School Teacher | (Level 3) Senior Educator

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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.


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




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

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


Express 36 with positive exponent.


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

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