What is (\partial)/(\partial y)(1/y) ?

The answer to (\partial)/(\partial y)(1/y) is -1/(y^2)

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(\partial)/(\partial y)(1/y)

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

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

Solution steps

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

Apply exponent rule:

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

= \frac{\partial}{\partial 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 (cos (\frac{1}{x - 1}))

t an g e n t y = x^{3} - 3 x + 3, (3, 21)

x \to \frac{π}{2} lim (\frac{sec ( x )}{sec ( 3 x )})

t an g e n t f (x) = 3 + 4 x^{2} - 2 x^{3}, at x = a

(y + 4) y^{^{'}} = 2 x y + 4 y, y (2) = 1

What is (\partial)/(\partial y)(1/y) ?
The answer to (\partial)/(\partial y)(1/y) is -1/(y^2)