Would the answer be A(-n)= A-n
When doing the product rule?
not sure about it help if you can thank you.
No. A times -n is -An
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To determine if the answer to the product rule is A(-n) = A-n, let's first review what the product rule states.
The product rule is a formula used for finding the derivative of the product of two functions. It states that if we have two functions, u(x) and v(x), then the derivative of their product, u(x)v(x), is given by:
(d/dx)(u(x)v(x)) = u(x)(d/dx)(v(x)) + v(x)(d/dx)(u(x))
Now, let's apply the product rule to the specific scenario you mentioned. You have A(-n) and you want to find its derivative.
Following the product rule, we can let u(x) = A and v(x) = -n. Taking the derivative of each:
(d/dx)(A(-n)) = A(d/dx)(-n) + (-n)(d/dx)(A)
Since (-n) is a constant with respect to x, (d/dx)(-n) equals zero. Also, since A is a function of x, (d/dx)(A) represents the derivative of A with respect to x.
Therefore, we have:
(d/dx)(A(-n)) = 0 - n(A')
Simplifying this expression, we get:
(d/dx)(A(-n)) = -n(A')
So, the correct answer should be: (d/dx)(A(-n)) = -n(A')
In conclusion, the answer A(-n) = A-n is not correct when applying the product rule. Instead, the correct answer is (d/dx)(A(-n)) = -n(A').