What is the derivative of arctan(sx) ?

The derivative of arctan(sx) is s/(s^2x^2+1)

What is the first derivative of arctan(sx) ?

The first derivative of arctan(sx) is s/(s^2x^2+1)

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

\frac{s}{s ^{2} x ^{2} + 1}

Solution steps

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

Apply the chain rule:

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

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

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

= \frac{1}{( s x ) ^{2} + 1} s

Simplify

\frac{1}{( s x ) ^{2} + 1} s : \frac{s}{s ^{2} x ^{2} + 1}

= \frac{s}{s ^{2} x ^{2} + 1}

\frac{d}{d x} (tan (x - y))

3 cos (8 t)

y^{^{''}} - 2 y - 8 y = 0, y (0) = - 2, y^{^{'}} (0) = 4

\int - 4 sin (2 t) d t

What is the derivative of arctan(sx) ?
The derivative of arctan(sx) is s/(s^2x^2+1)
What is the first derivative of arctan(sx) ?
The first derivative of arctan(sx) is s/(s^2x^2+1)