`y = (x^2 + 2)^2 (x^4 + 4)^4` Use logarithmic differentiation to find the derivative of the function.

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mathace eNotes educator| Certified Educator

Given: `y=(x^2+2)^2(x^4+4)^4`      Take the logarithm of both sides of the equation, then rewrite the expression using the laws of logarithms. ``



Take the derivate of both sides of the equation. 



Substitute in for y using the given. 


The derivative is: `(4x)(x^2+2)(x^4+4)^4+(16x^3)(x^2+2)^2(x^4+4)^3`