Final Answer
$2\left(y-1\right)\left(y^2+y+1\right)^2\left(y^3+1\right)^2+\left(y-1\right)^2\left(2\left(y^2+y+1\right)\left(2y+1\right)\left(y^3+1\right)^2+6\left(y^2+y+1\right)^2\left(y^3+1\right)y^{2}\right)-6y^{5}y^6+6\left(-y^6+2\right)y^{5}$
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Step-by-step Solution
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Simplifying
$\frac{d}{dy}\left(\left(\left(y-1\right)\left(y^2+y+1\right)\right)^2\left(y^3+1\right)^2+\left(-y^6+2\right)y^6\right)$
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$\frac{d}{dy}\left(\left(\left(y-1\right)\left(y^2+y+1\right)\right)^2\left(y^3+1\right)^2+\left(-y^6+2\right)y^6\right)$
Learn how to solve problems step by step online. Find the derivative of ((y-1)(y^2+y+1))^2(y^3+1)^2-y^6(y^6-2). Simplifying. The power of a product is equal to the product of it's factors raised to the same power. The derivative of a sum of two or more functions is the sum of the derivatives of each function. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=\left(y-1\right)^2 and g=\left(y^2+y+1\right)^2\left(y^3+1\right)^2.
Final Answer
$2\left(y-1\right)\left(y^2+y+1\right)^2\left(y^3+1\right)^2+\left(y-1\right)^2\left(2\left(y^2+y+1\right)\left(2y+1\right)\left(y^3+1\right)^2+6\left(y^2+y+1\right)^2\left(y^3+1\right)y^{2}\right)-6y^{5}y^6+6\left(-y^6+2\right)y^{5}$