What is the derivative of sqrt(x^2+16) ?

The derivative of sqrt(x^2+16) is x/(sqrt(x^2+16))

What is the first derivative of sqrt(x^2+16) ?

The first derivative of sqrt(x^2+16) is x/(sqrt(x^2+16))

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derivative of

x^{2} + 16

\frac{x}{x ^{2} + 16}

Solution steps

\frac{d}{d x} (x^{2} + 16)

Apply the chain rule:

\frac{1}{2 x ^{2} + 16} \frac{d}{d x} (x^{2} + 16)

= \frac{1}{2 x ^{2} + 16} \frac{d}{d x} (x^{2} + 16)

\frac{d}{d x} (x^{2} + 16) = 2 x

= \frac{1}{2 x ^{2} + 16} \cdot 2 x

Simplify

\frac{1}{2 x ^{2} + 16} \cdot 2 x : \frac{x}{x ^{2} + 16}

= \frac{x}{x ^{2} + 16}

What is the derivative of sqrt(x^2+16) ?
The derivative of sqrt(x^2+16) is x/(sqrt(x^2+16))
What is the first derivative of sqrt(x^2+16) ?
The first derivative of sqrt(x^2+16) is x/(sqrt(x^2+16))