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Popular >

derivative of sqrt((x^2/4+17))

Solution

\frac{d}{d x} (\frac{x ^{2}}{4} + 17)

Solution

\frac{x}{2 x ^{2} + 68}

Solution steps

\frac{d}{d x} (\frac{x ^{2}}{4} + 17)

Apply the chain rule:

\frac{1}{2 \frac{x ^{2}}{4} + 17} \frac{d}{d x} (\frac{x ^{2}}{4} + 17)

= \frac{1}{2 \frac{x ^{2}}{4} + 17} \frac{d}{d x} (\frac{x ^{2}}{4} + 17)

\frac{d}{d x} (\frac{x ^{2}}{4} + 17) = \frac{x}{2}

= \frac{1}{2 \frac{x ^{2}}{4} + 17} \cdot \frac{x}{2}

Simplify

\frac{1}{2 \frac{x ^{2}}{4} + 17} \cdot \frac{x}{2} : \frac{x}{2 x ^{2} + 68}

= \frac{x}{2 x ^{2} + 68}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of sqrt((x^2/4+17)) ?
The derivative of sqrt((x^2/4+17)) is x/(2sqrt(x^2+68))
What is the first derivative of sqrt((x^2/4+17)) ?
The first derivative of sqrt((x^2/4+17)) is x/(2sqrt(x^2+68))