Question

Differentiate. f(y) = 1 y2 − 5 y4 (y 9y3)

a) f'(y) = -2/y³ - 45y⁴y³+1
b) f'(y) = -2/y³ - 45y⁹y³+1
c) f'(y) = 2/y³ - 45y⁴y³+1
d) f'(y) = 2/y³ - 45y⁹y³+1

Answer 1

The question asks for the derivative of a function which appears to contain some errors. Applying the power rule for differentiation, the correct derivative of the function
`f(y) = 1/y^2 - 5y^4 is f'(y) = -2/y^3 - 20y^3.`

Step-by-step explanation:

The question seems to contain some typographical errors, but it appears to be asking to differentiate the function f(y). The correct process to differentiate the given function includes applying the power rule. Assuming the function is
`f(y) = (1)/(y^2) - 5y^4,` we differentiate each term separately.

The derivative of the first term
`(1)/(y^2)`using the power rule is
`-2/y^3,` as we bring down the exponent and subtract one from the power. For the second term,
`-5y^4,`the derivative is
`-20y^3`. Therefore, the correct derivative should be
`f'(y) = -2/y^3` -
`20y^3`. None of the provided options are correct.