What is the derivative of sqrt(-x^2+4) ?

The derivative of sqrt(-x^2+4) is -x/(sqrt(-x^2+4))

What is the first derivative of sqrt(-x^2+4) ?

The first derivative of sqrt(-x^2+4) is -x/(sqrt(-x^2+4))

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

- \frac{x}{- x ^{2} + 4}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

\frac{1}{2 - x ^{2} + 4} (- 2 x) : - \frac{x}{- x ^{2} + 4}

= - \frac{x}{- x ^{2} + 4}

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