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Step-by-step Solution

Find the derivative of $\sqrt{\frac{x^{\left(2-5\right)}}{10-x^2}}$ using the constant rule

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Answer

$\frac{1}{2}\left(\frac{x^{-3}}{10-x^2}\right)^{-\frac{1}{2}}\left(\frac{-3x^{-4}\left(10-x^2\right)+2x^{-2}}{\left(10-x^2\right)^2}\right)$

Step-by-step explanation

Problem to solve:

$\frac{d}{dx}\left(\sqrt{\frac{x^{\left(2-5\right)}}{10-x^2}}\right)$
1

Subtract the values $2$ and $-5$

$\frac{d}{dx}\left(\sqrt{\frac{x^{-3}}{10-x^2}}\right)$
2

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

$\frac{1}{2}\left(\frac{x^{-3}}{10-x^2}\right)^{-\frac{1}{2}}\cdot\frac{d}{dx}\left(\frac{x^{-3}}{10-x^2}\right)$

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Answer

$\frac{1}{2}\left(\frac{x^{-3}}{10-x^2}\right)^{-\frac{1}{2}}\left(\frac{-3x^{-4}\left(10-x^2\right)+2x^{-2}}{\left(10-x^2\right)^2}\right)$
$\frac{d}{dx}\left(\sqrt{\frac{x^{\left(2-5\right)}}{10-x^2}}\right)$

Main topic:

Constant rule

Used formulas:

5. See formulas

Time to solve it:

~ 0.87 seconds