The curve C has the equation: y=3x^2*(x+2)^6 Find dy/dx
To find dy/dx, we must use a combination of the Product Rule and the Chain Rule.
If we let 3x^2=u and (x+2)^6=v, the Product Rule tells us that (uv)' = uv'+vu'
u'=6x, but to find v' we need to use the Chain Rule:
The Chain rule states that d/dx f(g(x)) = f'(g(x))g'(x)
(x+2)^6 can be written in the form f(g(x)) where f(x)=x^6 and g(x)=x+2, it follows that f'(x)=6x^5 and g'(x)=1
We can now see that v'=6(x+2)^51
Putting all this together, we find that (uv)'= 3x^26(x+2)^5 + (x+2)^66x
= 18x^2(x+2)^5 + 6x(x+2)^6
SH
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