What is the derivative of arctan(9/x)+arctan(3/x) ?

The derivative of arctan(9/x)+arctan(3/x) is (-12x^2-324)/((x^2+9)(x^2+81))

What is the first derivative of arctan(9/x)+arctan(3/x) ?

The first derivative of arctan(9/x)+arctan(3/x) is (-12x^2-324)/((x^2+9)(x^2+81))

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derivative of

arctan (\frac{9}{x}) + arctan (\frac{3}{x})

\frac{- 12 x ^{2} - 324}{( x ^{2} + 9 ) ( x ^{2} + 81 )}

Solution steps

\frac{d}{d x} (arctan (\frac{9}{x}) + arctan (\frac{3}{x}))

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (arctan (\frac{9}{x})) + \frac{d}{d x} (arctan (\frac{3}{x}))

\frac{d}{d x} (arctan (\frac{9}{x})) = - \frac{9}{81 + x ^{2}}

\frac{d}{d x} (arctan (\frac{3}{x})) = - \frac{3}{9 + x ^{2}}

= - \frac{9}{81 + x ^{2}} - \frac{3}{9 + x ^{2}}

Simplify

- \frac{9}{81 + x ^{2}} - \frac{3}{9 + x ^{2}} : \frac{- 12 x ^{2} - 324}{( x ^{2} + 9 ) ( x ^{2} + 81 )}

= \frac{- 12 x ^{2} - 324}{( x ^{2} + 9 ) ( x ^{2} + 81 )}

\frac{s + 3}{s ^{2} + 6 s + 10}

\frac{d}{d x} (5^{x} + 5 cos (\frac{5 x}{2}))

\int \frac{5 + t + t ^{2}}{t} d t

x \frac{d y}{d x} = y - \frac{1}{y}

x \to - 5 - lim (\frac{∣ x + 5 ∣}{x + 5})

What is the derivative of arctan(9/x)+arctan(3/x) ?
The derivative of arctan(9/x)+arctan(3/x) is (-12x^2-324)/((x^2+9)(x^2+81))
What is the first derivative of arctan(9/x)+arctan(3/x) ?
The first derivative of arctan(9/x)+arctan(3/x) is (-12x^2-324)/((x^2+9)(x^2+81))