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The math problem asks to find the derivative of the function $$y=(x+1)^4(x+5)^2$$

I get to the part $$(x+1)^4 \cdot 2(x+5) + (x+5)^2 \cdot 4(x+1)^3$$

How do they arrive at the answer

$$2(x+1)^3(x+5)(3x+11) ?$$

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    By taking the factor $(x+1)^3(x+5)$. – 2017-01-29
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    Many texts will factor or expand. Don't worry if your answer doesn't exactly match. – 2017-01-29
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    ^ always plug and check to see if your answer is correct – 2017-01-29

2 Answers 2

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$$\begin{align}(x+1)^4 \cdot 2(x+5) + (x+5)^2 \cdot 4(x+1)^3&=(x+1)^3(x+5)\cdot\big[(x+1)2+(x+5)4\big]\\ &=(x+1)^3(x+5)\cdot\big[2x+2+4x+20 \big]\\ &=(x+1)^3(x+5)\cdot(6x+22)\\ &=(x+1)^3(x+5)\cdot 2(3x+11)\end{align}$$

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    @Fiona Lu There are now two answers in your question. You can either accept mine or the other by simply clicking the check mark. The upward arrow is for up vote if you wish to. – 2017-01-29
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$$(x+1)^4 \cdot 2(x+5) + (x+5)^2 \cdot 4(x+1)^3$$

$$(x+1)^3((x+1) \cdot 2(x+5) + (x+5)^2 \cdot 4)$$

$$(x+1)^3(x+5)( (x+1)\cdot 2 + (x+5) \cdot 4)$$

$$(x+1)^3(x+5)( 2)((x+1)+ (x+5)2)$$

$$2(x+1)^3(x+5)(x+1+2x+10)$$

$$2(x+1)^3(x+5)(3x + 11)$$

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    Thanks a lot for your help! – 2017-01-29