What is the derivative of sec(arctan(x)) ?

The derivative of sec(arctan(x)) is x/(sqrt(1+x^2))

What is the first derivative of sec(arctan(x)) ?

The first derivative of sec(arctan(x)) is x/(sqrt(1+x^2))

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

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

Solution steps

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

Simplify

sec (arctan (x)) : 1 + x^{2}

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

Apply the chain rule:

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

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

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

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

Simplify

\frac{1}{2 1 + x ^{2}} \cdot 2 x : \frac{x}{1 + x ^{2}}

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

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