What is the derivative of 1/(4y^2) ?

The derivative of 1/(4y^2) is -1/(2y^3)

What is the first derivative of 1/(4y^2) ?

The first derivative of 1/(4y^2) is -1/(2y^3)

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derivative of

\frac{1}{4 y ^{2}}

- \frac{1}{2 y ^{3}}

Solution steps

\frac{d}{d y} (\frac{1}{4 y ^{2}})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{1}{4} \frac{d}{d y} (\frac{1}{y ^{2}})

Apply exponent rule:

\frac{1}{a} = a^{- 1}

= \frac{1}{4} \frac{d}{d y} (y^{- 2})

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= \frac{1}{4} (- 2 y^{- 2 - 1})

Simplify

\frac{1}{4} (- 2 y^{- 2 - 1}) : - \frac{1}{2 y ^{3}}

= - \frac{1}{2 y ^{3}}

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What is the derivative of 1/(4y^2) ?
The derivative of 1/(4y^2) is -1/(2y^3)
What is the first derivative of 1/(4y^2) ?
The first derivative of 1/(4y^2) is -1/(2y^3)