What is the derivative of arctan(9t) ?

The derivative of arctan(9t) is 9/(81t^2+1)

What is the first derivative of arctan(9t) ?

The first derivative of arctan(9t) is 9/(81t^2+1)

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derivative of

arctan (9 t)

\frac{9}{81 t ^{2} + 1}

Solution steps

\frac{d}{d t} (arctan (9 t))

Apply the chain rule:

\frac{1}{( 9 t ) ^{2} + 1} \frac{d}{d t} (9 t)

= \frac{1}{( 9 t ) ^{2} + 1} \frac{d}{d t} (9 t)

\frac{d}{d t} (9 t) = 9

= \frac{1}{( 9 t ) ^{2} + 1} \cdot 9

Simplify

\frac{1}{( 9 t ) ^{2} + 1} \cdot 9 : \frac{9}{81 t ^{2} + 1}

= \frac{9}{81 t ^{2} + 1}

\int_{0}^{2} x^{2} e^{- 9 x} d x

\frac{d}{d x} (6 (sec (x) - tan (x))^{\frac{3}{2}})

x^{2} - 11, 10 x, [- 11, 0] y = 0

\frac{d}{d x} (- 1 0^{3 x^{2} - 4})

What is the derivative of arctan(9t) ?
The derivative of arctan(9t) is 9/(81t^2+1)
What is the first derivative of arctan(9t) ?
The first derivative of arctan(9t) is 9/(81t^2+1)