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

f (x) = \frac{3 x}{x ^{2} - 2}, at x = 1

\int \frac{1}{x ( x + 2 ) ( x - 3 )} d x

\int_{- \infty}^{0} \frac{1}{3 - 5 x} d x

\int \frac{x ^{3} + 21}{x ^{2} + 5 x + 6} d x

\frac{\partial}{\partial x} (a x^{b} y^{1 - b})

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))