What is the derivative of sqrt(x\sqrt{x^2+1)} ?

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

What is the first derivative of sqrt(x\sqrt{x^2+1)} ?

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

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derivative of

x x^{2} + 1

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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

\frac{d}{d x} (\frac{1}{x ^{3} + 2})

x \to 2 lim (x^{3} - 2 x^{2} + x - 3)

(2 - 3 x^{2})^{4} (x^{7} + 3)^{3}

f (x) = \frac{x}{4}

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