What is the d/(dy)(arctan(xy)) ?

The d/(dy)(arctan(xy)) is x/(x^2y^2+1)

What is the first d/(dy)(arctan(xy)) ?

The first d/(dy)(arctan(xy)) is x/(x^2y^2+1)

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

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

Solution steps

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

Treat

x

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int - 15 d x

\frac{d}{d x} (x cos (t))

\int \frac{1}{e ^{z}} d z

T \to 9 0^{\circ} lim (f (T))

\frac{\partial}{\partial x} (\frac{4}{3} π x^{3})

What is the d/(dy)(arctan(xy)) ?
The d/(dy)(arctan(xy)) is x/(x^2y^2+1)
What is the first d/(dy)(arctan(xy)) ?
The first d/(dy)(arctan(xy)) is x/(x^2y^2+1)