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

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

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

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

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

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

Solution steps

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

Treat

C

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

\frac{d C}{d x} = 0

= \frac{x}{( x ^{2} - 1 ) x ^{2} - 2} + 0

Simplify

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

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

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

\frac{1}{s ^{2} ( s ^{2} + 16 )}

\int 9 sin^{6} (z) d z

\frac{d}{d x} (6 x + 7)

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