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

Derive the function (x^2y^2)/(x^4+y^4) with respect to x

Answer

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

Step-by-step explanation

Problem

$\frac{d}{dx}\left(\frac{x^2 y^2}{x^4+y^4}\right)$
1

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 ${\displaystyle h'(x) = \frac{f'(x) \cdot g(x) - g'(x) \cdot f(x)}{g(x)^2}}$

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

Unlock this step-by-step solution!

Answer

$\frac{2y^2x\left(y^4+x^4\right)-4y^2x^2x^{3}}{\left(y^4+x^4\right)^2}$
$\frac{d}{dx}\left(\frac{x^2 y^2}{x^4+y^4}\right)$

Main topic:

Differential calculus

Used formulas:

5. See formulas

Time to solve it:

~ 0.3 seconds