SOLUTION: Expand each function (using the appropriate technique/formula). Compute the derivative of the expanded function by applying the differentiation rules. 1.f(x)= (x+5)^2 2.f(x)

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Question 1192774: Expand each function (using the appropriate technique/formula). Compute the derivative of the expanded function by applying the differentiation rules.
1.f(x)= (x+5)^2
2.f(x)= (x^2+2x+3)^2
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Use the chain rule,
u=x%2B5
df%2Fdx=%28df%2Fdu%29%28du%2Fdx%29
So,
f=u%5E2
df%2Fdu=2u
and
u=x%2B5
du%2Fdx=1
So then,
df%2Fdx=%282u%29%281%29
df%2Fdx=2%28x%2B5%29
df%2Fdx=2x%2B10
.
.
.
Similarly,
v=x%5E2%2B2x%2B3
df%2Fdx=%28df%2Fdv%29%28dv%2Fdx%29
So,
f=v%5E2
df%2Fdv=2v
and
v=x%5E2%2B2x%2B3
dv%2Fdx=2x%2B2
So then,
df%2Fdx=%282v%29%282x%2B2%29
df%2Fdx=2%28x%5E2%2B2x%2B3%29%282%28x%2B1%29%29
df%2Fdx=4%28x%5E2%2B2x%2B3%29%28x%2B1%29