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

The derivative of sqrt(r^2-x^2) is (r\frac{dr)/(dx)-x}{sqrt(r^2-x^2)}

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

The first derivative of sqrt(r^2-x^2) is (r\frac{dr)/(dx)-x}{sqrt(r^2-x^2)}

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\frac{d}{d x} (r (x)^{2} - x^{2})

\frac{r \frac{d r}{d x} - x}{r ^{2} - x ^{2}}

Solution steps

\frac{d}{d x} (r^{2} - x^{2})

Apply the chain rule:

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

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

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

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

Simplify

\frac{1}{2 r ^{2} - x ^{2}} (2 r \frac{d r}{d x} - 2 x) : \frac{r \frac{d r}{d x} - x}{r ^{2} - x ^{2}}

= \frac{r \frac{d r}{d x} - x}{r ^{2} - x ^{2}}

What is the derivative of sqrt(r^2-x^2) ?
The derivative of sqrt(r^2-x^2) is (r\frac{dr)/(dx)-x}{sqrt(r^2-x^2)}
What is the first derivative of sqrt(r^2-x^2) ?
The first derivative of sqrt(r^2-x^2) is (r\frac{dr)/(dx)-x}{sqrt(r^2-x^2)}