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

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

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

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

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

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

Solution steps

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

Treat

t

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{d}{d x} (\frac{2 x - 4}{3 e ^{x}})

x \to 3 lim (\frac{1}{( x ^{2} - 9 )})

\int 2 x e^{- 2 x^{2}} d x

f (x) = x^{5} \cdot e^{x}

n = 1 \sum \infty \frac{( x + 3 ) ^{n}}{n}

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