What is the derivative of arctan((13/x)-arctan(3/x)) ?

The derivative of arctan((13/x)-arctan(3/x)) is (-10x^2+390)/((x^2+9)(x^2+169))

What is the first derivative of arctan((13/x)-arctan(3/x)) ?

The first derivative of arctan((13/x)-arctan(3/x)) is (-10x^2+390)/((x^2+9)(x^2+169))

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\frac{d}{d x} (arctan (\frac{13}{x}) - arctan (\frac{3}{x}))

\frac{- 10 x ^{2} + 390}{( x ^{2} + 9 ) ( x ^{2} + 169 )}

Solution steps

\frac{d}{d x} (arctan (\frac{13}{x}) - arctan (\frac{3}{x}))

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (arctan (\frac{13}{x})) - \frac{d}{d x} (arctan (\frac{3}{x}))

\frac{d}{d x} (arctan (\frac{13}{x})) = - \frac{13}{169 + x ^{2}}

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

= - \frac{13}{169 + x ^{2}} - (- \frac{3}{9 + x ^{2}})

Simplify

- \frac{13}{169 + x ^{2}} - (- \frac{3}{9 + x ^{2}}) : \frac{- 10 x ^{2} + 390}{( x ^{2} + 9 ) ( x ^{2} + 169 )}

= \frac{- 10 x ^{2} + 390}{( x ^{2} + 9 ) ( x ^{2} + 169 )}

\frac{\partial}{\partial x} (x e^{y^{2}} - y e^{x^{2}})

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

x \to 4 lim (4 - x)

\int csc (- 4 x) d x

\int \frac{( ln ^{2} ( x ) )}{x ^{2}} d x

What is the derivative of arctan((13/x)-arctan(3/x)) ?
The derivative of arctan((13/x)-arctan(3/x)) is (-10x^2+390)/((x^2+9)(x^2+169))
What is the first derivative of arctan((13/x)-arctan(3/x)) ?
The first derivative of arctan((13/x)-arctan(3/x)) is (-10x^2+390)/((x^2+9)(x^2+169))