What is the derivative of 1/y ?

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

What is the first derivative of 1/y ?

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

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derivative of

\frac{1}{y}

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

Solution steps

\frac{d}{d y} (\frac{1}{y})

Apply exponent rule:

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

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

Apply the Power Rule:

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

= - 1 \cdot y^{- 1 - 1}

Simplify

- 1 \cdot y^{- 1 - 1} : - \frac{1}{y ^{2}}

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

x \to 1 lim (\frac{e ^{x}}{2})

f (x) = cos (x^{5})

\frac{\partial}{\partial x} (p (x)^{2})

y = \frac{x}{5}, y = 1, x = 0

x \to - 2 lim (- x^{2} + 4 x - 1)