What is the derivative of arctan(sqrt(1+x^2)) ?

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

(\frac{100}{ln ( 2 x + 1 )})^{^{'}}

\int 2 y^{2} ln (y) d y

7 e^{x^{2}}

\int \frac{tan ^{2} ( x )}{sin ( x )} d x

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

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