What is (\partial)/(\partial x)(((x^2))/(y^2+1)) ?

The answer to (\partial)/(\partial x)(((x^2))/(y^2+1)) is (2x)/(y^2+1)

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(\partial)/(\partial x)(((x^2))/(y^2+1))

\frac{\partial}{\partial x} (\frac{( x ^{2} )}{y ^{2} + 1})

\frac{2 x}{y ^{2} + 1}

Solution steps

\frac{\partial}{\partial x} (\frac{( x ^{2} )}{y ^{2} + 1})

Treat

y

as a constant

Take the constant out:

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

= \frac{1}{y ^{2} + 1} \frac{\partial}{\partial x} (x^{2})

Apply the Power Rule:

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

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

Simplify

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

= \frac{2 x}{y ^{2} + 1}

f^{^{'}} (x) = 3 (1 - 2 x)^{2}

x \to 4 lim (\frac{x}{x ^{2} - 15})

\int - x^{2} - x + 2 d x

\int_{0}^{1} \frac{x}{25 + 144 x ^{4}} d x

\frac{d}{d x} (cos (3 x - 1))

What is (\partial)/(\partial x)(((x^2))/(y^2+1)) ?
The answer to (\partial)/(\partial x)(((x^2))/(y^2+1)) is (2x)/(y^2+1)