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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

= cos (arctan (x)) \frac{d}{d x} (arctan (x))

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

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

Simplify

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

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

\int x 2^{x^{2}} d x

\int + \frac{x}{x ^{4} + 7} d x

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

\int_{0}^{\frac{1}{2}} 8 arccos (x) d x

x \to 0 lim (- ln (x))

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