Use Quotient Rule to differentiate f(v)=2v/v^5+2

Question

2v/v⁵+2

I got -8v⁵+4/(v⁵+2)²

Is this correct?

Or should it be -8v⁵/5v²

^{since numbers = 0 when derived ?}

Thanks.

Answer 1

Hello, To find the derivative, you will use the quotient rule:

If h(x) = f(x)/g(x), then h'(x) = [g(x) · f'(x) - f(x) · g'(x)] / [g(x)]².

So, for this function, the derivative will be [(v⁵+ 2) · 2 - 2v · 5v⁴]/ (v⁵+ 2)², which will simplify to your first answer:

[-8v⁵ + 4]/(v⁵ + 2)²

You are correct that the derivative of a constant is zero, but at the point of the expression above, you have ALREADY taken the derivative of the function.

I hope this helps. Please let me know if you have any further questions.

Answer 2

(-8v⁵+4) / (v⁵+2)²

is correct