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Step-by-step Solution

Derive the function $-\left(\frac{x^2}{y^2}\right)$ with respect to x

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Answer

$\frac{-2x}{y^{2}}$

Step-by-step explanation

Problem to solve:

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

The derivative of a function multiplied by a constant is equal to the constant times the derivative of the function

$-\frac{d}{dx}\left(\frac{x^2}{y^2}\right)$
2

Applying the quotient rule which states that if $f(x)$ and $g(x)$ are functions and $h(x)$ is the function defined by ${\displaystyle h(x) = \frac{f(x)}{g(x)}}$, where ${g(x) \neq 0}$, then ${\displaystyle h'(x) = \frac{f'(x) \cdot g(x) - g'(x) \cdot f(x)}{g(x)^2}}$

$-\left(\frac{y^2\frac{d}{dx}\left(x^2\right)-x^2\frac{d}{dx}\left(y^2\right)}{y^{4}}\right)$

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Answer

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

Main topic:

Differential calculus

Used formulas:

4. See formulas

Time to solve it:

~ 0.55 seconds