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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int 5 x x^{2} + 1 d x

y^{^{''}} - 2 y^{^{'}} - 11 y = 0

s (t) = \frac{5}{t ^{2} + 6 t - 8}

\int \frac{x + 4}{x ^{8}} d x

\frac{d}{d x} (7 x e^{- x})

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