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# Find the derivative of the function. f(x) = (2x - 2)^{4 }(x^{2}+x+1)^{5}.

**Solution:**

Given function f(x) = (2x − 2)^{4} (x^{2} + x + 1)^{5}

To find the derivative of f(x), we use^{ }the product rule of differentiation for f(x)= g(x).h(x), we have

**f**′(x) = g′(x).h(x) +g(x).h′(x)

Here, g(x)=(2x-2)⁴ ; h(x) = (x^{2}+ x +1)⁵

Hence, g′(x) = 4(2x-2)³(2) = 8(2x-3)³

h′(x) = 5( x^{2}+ x +1)⁴(2x+1)

f′(x)= {8(2x-2)³}{(x^{2}+ x +1)⁵} + {(2x-3)⁴}{ 5( x^{2}+ x +1)⁴(2x+1)}

=(2x-2)³(x^{2}+ x +1)⁴{8(x^{2}+ x +1) + 5(2x-3)(2x+1)}

=(2x-2)³(x^{2}+ x +1)⁴ {8x^{2}+8x+8+20x^{2} -10x -10}

=(2x-2)³(x^{2}+ x +1)⁴ {28x^{2}-2x-2}

## Find the derivative of the function. f(x) = (2x - 2)^{4 }(x^{2}+x+1)^{5}.

**Summary:**

The derivative of the function. f(x) = (2x - 2)^{4 }(x^{2}+x+1)^{5} =(2x-2)³(x^{2}+ x +1)⁴ {28x^{2}-2x-2}

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