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

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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