What is the derivative of arctan(d/x) ?

The derivative of arctan(d/x) is -d/(d^2+x^2)

What is the first derivative of arctan(d/x) ?

The first derivative of arctan(d/x) is -d/(d^2+x^2)

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

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

Solution steps

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

Treat

d

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int (x - 1) e^{x} d x

y^{^{''}} + 2 y^{^{'}} = (8 t - 7) sin (3 t)

\int e^{2 t} d t

\frac{\partial}{\partial y} (x^{3} cos (y))

x \to 0 lim (5 x^{2})

What is the derivative of arctan(d/x) ?
The derivative of arctan(d/x) is -d/(d^2+x^2)
What is the first derivative of arctan(d/x) ?
The first derivative of arctan(d/x) is -d/(d^2+x^2)