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

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

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

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

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derivative of

arctan (\frac{3 + t}{3 - t})

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

x \to 0 + lim (x^{7 s i n (x)})

\frac{d}{d x} (3^{4 x + 1})

x = y, 2 x + y^{2} = 8

\int_{0}^{3} \frac{1}{x x + 1} d x

\frac{1}{s ( s ^{2} + 4 s + 5 )}

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