Tutorial Exercise
Differentiate the function.
\(F(y) = \left(\frac{1}{y^2} - \frac{4}{y^4}\right)(y + 2y^3)\)
Step 1
To find the derivative of the product \(F(y) = \left(\frac{1}{y^2} - \frac{4}{y^4}\right)(y + 2y^3)\), we will use the P
\(\frac{d}{dy}[f(y)g(y)] = f'(y)g(y) + f(y)g'(y).\)
First, we rewrite the first term of the product as follows.
\(\frac{1}{y^2} - \frac{4}{y^4} = y^{-2} - 4y^{-4}\)
Step 2
The derivative of the first term, \(\frac{1}{y^2} - \frac{4}{y^4} = y^{-2} - 4y^{-4}\), is
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