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

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

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

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

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

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

Solution steps

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

Simplify

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{3}{4 x + 1}

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

\int \frac{5}{1 + 4 x ^{2}} d x

\int 6 x + 7 d x

\int \frac{3 x ^{2} + 4 x + 19}{( x + 3 ) ( x ^{2} + 25 )} d x

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