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Popular >

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

Solution

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

Solution

\frac{x}{x ^{2} - a ^{2}}

Solution steps

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

Apply the chain rule:

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

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

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

= \frac{1}{2 x ^{2} - a ^{2}} \cdot 2 x

Simplify

\frac{1}{2 x ^{2} - a ^{2}} \cdot 2 x : \frac{x}{x ^{2} - a ^{2}}

= \frac{x}{x ^{2} - a ^{2}}

Graph

Popular Examples

sum from n=0 to infinity of 1/(3^{n-1)}

n = 0 \sum \infty \frac{1}{3 ^{n - 1}}

y = \frac{1}{ln ( x )}

limit as x approaches 5 of x/(|x-5|)

x \to 5 lim (\frac{x}{∣ x - 5 ∣})

tangent of y=x^2-sqrt(x),(1,0)tangent of

y = x^{2} - x, (1, 0)

integral from 0 to pi of sin^2(5x)

\int_{0}^{π} sin^{2} (5 x) d x

Frequently Asked Questions (FAQ)

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