What is the derivative of arctan((x^2/y)) ?

The derivative of arctan((x^2/y)) is (2xy-x^2\frac{dy)/(dx)}{x^4+y^2}

What is the first derivative of arctan((x^2/y)) ?

The first derivative of arctan((x^2/y)) is (2xy-x^2\frac{dy)/(dx)}{x^4+y^2}

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

\frac{2 x y - x ^{2} \frac{d y}{d x}}{x ^{4} + y ^{2}}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{2 x y - x ^{2} \frac{d y}{d x}}{x ^{4} + y ^{2}}

t an g e n t 11 x^{\frac{1}{2}} + x^{\frac{3}{2}}

\int_{1}^{e} ln (5 x) d x

d er i v a t i v e x + 1

\frac{d}{d x} (∣ x ∣^{a})

\int \frac{1}{x ^{2} 36 x ^{2} - 1} d x

What is the derivative of arctan((x^2/y)) ?
The derivative of arctan((x^2/y)) is (2xy-x^2\frac{dy)/(dx)}{x^4+y^2}
What is the first derivative of arctan((x^2/y)) ?
The first derivative of arctan((x^2/y)) is (2xy-x^2\frac{dy)/(dx)}{x^4+y^2}