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

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

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(\partial)/(\partial x)(y^2arctan(x))

\frac{\partial}{\partial x} (y^{2} arctan (x))

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

Solution steps

\frac{\partial}{\partial x} (y^{2} arctan (x))

Treat

y

as a constant

Take the constant out:

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

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

Apply the common derivative:

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

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

Simplify

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

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

\frac{\partial}{\partial x} (\frac{x + y}{y - x})

x \to 0 lim (- x^{2} + 1)

\int_{1}^{25} 5 x e^{2 x} d x

\int_{1}^{2} \frac{( x ^{2} - 1 )}{x + 1} d x

f (x) = \frac{c x ^{2}}{x ^{2} + b}

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