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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (2 x^{2} + 1) = 4 x

= \frac{1}{2 2 x ^{2} + 1} \cdot 4 x

Simplify

\frac{1}{2 2 x ^{2} + 1} \cdot 4 x : \frac{2 x}{2 x ^{2} + 1}

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

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