What is the derivative of arctan(xy) ?

The derivative of arctan(xy) is (y+x\frac{dy)/(dx)}{x^2y^2+1}

What is the first derivative of arctan(xy) ?

The first derivative of arctan(xy) is (y+x\frac{dy)/(dx)}{x^2y^2+1}

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

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

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (x y) = y + x \frac{d y}{d x}

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

Simplify

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

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

\int \frac{( 3 x - 2 )}{5 x ^{2} - 3 x + 2} d x

f (x) = \frac{3}{1 + x ^{2}}

\int_{0}^{1} 3 x^{2} (x^{3} + 5)^{- 2} d x

\int sin (5 π) t d t

2 y^{^{''}} - 8 y = 0

What is the derivative of arctan(xy) ?
The derivative of arctan(xy) is (y+x\frac{dy)/(dx)}{x^2y^2+1}
What is the first derivative of arctan(xy) ?
The first derivative of arctan(xy) is (y+x\frac{dy)/(dx)}{x^2y^2+1}