SOLUTION: DIFFERENTIATE WITH RESPECT TO X (x - 3)(x+3)
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Question 235013: DIFFERENTIATE WITH RESPECT TO X (x - 3)(x+3)
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
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I presume you were given \ =\ (x\ -\ 3)(x\ +\ 3))
and you want to find )
One way (the hard way) to do this would be to say that \ =\ g(x)h(x))
where \ =\ (x\ -\ 3))
and \ =\ (x\ +\ 3))
.
Then use the product rule:
If , then \ =\ g'(x)h(x)\ +\ g(x)h'(x))
.
For your function, using the sum and power rules:
\ =\ (x\ -\ 3)\ \Rightarrow\ g'(x)\ =\ 1)
and
\ =\ (x\ +\ 3)\ \Rightarrow\ h'(x)\ =\ 1)
Therefore
\ = 1\,\cdot\,(x\ +\ 3)\ +\ (x\ -\ 3)\,\cdot\,1\ =\ 2x)
The easy way is to just multiply \ =\ (x\ -\ 3)(x\ + 3)\ = x^2\ -\ 9)
Then apply the sum rule and the power rule to say \ = 2x)
John
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