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

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

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

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

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

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

\frac{d}{d x} (2) = 0

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

Simplify

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

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