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

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

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

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

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

\frac{3}{x ^{2} + 9}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (\frac{3 + x}{3 - x}) = \frac{6}{( 3 - x ) ^{2}}

= \frac{1}{( \frac{3 + x}{3 - x} ) ^{2} + 1} \cdot \frac{6}{( 3 - x ) ^{2}}

Simplify

\frac{1}{( \frac{3 + x}{3 - x} ) ^{2} + 1} \cdot \frac{6}{( 3 - x ) ^{2}} : \frac{3}{x ^{2} + 9}

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

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

\int_{0}^{2} (8 t i - t^{3} j + 2 t^{3} k) d t

\int_{0}^{\frac{π}{6}} tan (3 x) d x

n = 1 \sum \infty \frac{ln ( n )}{n !}

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

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