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Popular >

derivative of sqrt(r^2-x^2)

Solution

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

Solution

\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}}

Popular Examples

sum from n=1 to infinity of 2/(2^n+5)

n = 1 \sum \infty \frac{2}{2 ^{n} + 5}

derivative of (0.14x/(0.15+x))

\frac{d}{d x} (\frac{0.14 x}{0.15 + x})

integral of (6ln(x+7))/(x^2)

\int \frac{6 ln ( x + 7 )}{x ^{2}} d x

(\partial)/(\partial x)(10^{x^2+x})

\frac{\partial}{\partial x} (1 0^{x^{2} + x})

tangent of y= 4/x tangent of

y = \frac{4}{x}

Frequently Asked Questions (FAQ)

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)}