Step-by-step Solution

Find the derivative $\frac{d}{dy}\left(y^{-\left(\frac{1}{2}\right)}\right)$ using the power rule

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Final Answer

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

Step-by-step explanation

Problem to solve:

$\frac{d}{dy}\left(y^{\left(-1\right)\cdot\frac{1}{2}}\right)$

Choose the solving method

1

The power rule for differentiation states that if $n$ is a real number and $f(x) = x^n$, then $f'(x) = nx^{n-1}$

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

Applying the property of exponents, $\displaystyle a^{-n}=\frac{1}{a^n}$, where $n$ is a number

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

Final Answer

$\frac{-\frac{1}{2}}{\sqrt{y^{3}}}$
$\frac{d}{dy}\left(y^{\left(-1\right)\cdot\frac{1}{2}}\right)$

Main topic:

Power rule

Related formulas:

1. See formulas

Time to solve it:

~ 0.03 s (SnapXam)