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

The answer to (\partial)/(\partial x)(arctan(x^2)) is (2x)/(x^4+1)

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

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

\frac{2 x}{x ^{4} + 1}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

\frac{1}{( x ^{2} ) ^{2} + 1} \cdot 2 x : \frac{2 x}{x ^{4} + 1}

= \frac{2 x}{x ^{4} + 1}

\frac{25 - x ^{2}}{4 x}

4 x - x^{2}, x^{2}

\int 1500 + \frac{3}{2} x + \frac{3}{10} x^{2} + \frac{4}{3} x^{3} d x

y^{^{''}} - y^{^{'}} - 2 y = 4 x^{2}

x \to - 4 lim ((2 x + 3) (x^{2} - 1))

What is (\partial)/(\partial x)(arctan(x^2)) ?
The answer to (\partial)/(\partial x)(arctan(x^2)) is (2x)/(x^4+1)