How do you differentiate #y = (x + 7)^10 (x^2 + 2)^7#?

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Answer 1 · 2016-01-18T14:56:40

See the explanation section, below.

For #y=f*g#, we have #y' = f'g+fg'#

In this problem, #f=(x+7)^10#, so #f' = 10(x+7)^9#,

and #g=(x^2+2)^7#, so #g' = 7(x^2+2)^6(2x)# #" "# #" "# (chain rule).

Therefore,

#y' = [10(x+7)^9] (x^2+2)^7 + (x+7)^10[7(x^2+2)^6(2x)]#.

Now use algebra to simplify as desired.

#y' = 10(x+7)^9 (x^2+2)^7 + 14x (x+7)^10 (x^2+2)^6#

# = 2(x+7)^9 (x^2+2)^6(12x^2+49x+10)#.