What is (\partial)/(\partial x)(-(2x^2)/(5y^2)) ?

The answer to (\partial)/(\partial x)(-(2x^2)/(5y^2)) is -(4x)/(5y^2)

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(\partial)/(\partial x)(-(2x^2)/(5y^2))

\frac{\partial}{\partial x} (- \frac{2 x ^{2}}{5 y ^{2}})

- \frac{4 x}{5 y ^{2}}

Solution steps

\frac{\partial}{\partial x} (- \frac{2 x ^{2}}{5 y ^{2}})

Treat

y

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= - \frac{2}{5 y ^{2}} \frac{\partial}{\partial x} (x^{2})

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= - \frac{2}{5 y ^{2}} \cdot 2 x^{2 - 1}

Simplify

- \frac{2}{5 y ^{2}} \cdot 2 x^{2 - 1} : - \frac{4 x}{5 y ^{2}}

= - \frac{4 x}{5 y ^{2}}

x \to 0 lim (\frac{( 1 + x ) ^{5} - 1}{x})

y \to - 3 lim (lo g_{2} (3) y^{2})

\int \frac{r ^{3}}{1 + r ^{2}} d r

\int_{0}^{4} x 4 - x d x

x \to \infty lim (\frac{( x + 1 ) ^{2} e ^{x^{3}}}{e ^{(x + 1)^{3}} x ^{2}})

What is (\partial)/(\partial x)(-(2x^2)/(5y^2)) ?
The answer to (\partial)/(\partial x)(-(2x^2)/(5y^2)) is -(4x)/(5y^2)