In mathematics, an isometry is a distance-preserving injective map between metric spaces. A composition of two opposite isometries is a direct <span>isometry.
Hope it helped!!</span>

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3 years ago

Why the derivative of (x^2/a^2) = (2x/a^2)?

Neko [114]

I assume you're referring to a function,

$f(x) = \dfrac{x^2}{a^2}$

where <em>a</em> is some unknown constant. By definition of the derivative,

$\displaystyle f'(x) = \lim_{h\to0}{f(x+h)-f(x)}h$

Then

$\displaystyle f'(x) = \lim_{h\to0}{\frac{(x+h)^2}{a^2}-\frac{x^2}{a^2}}h \\\\ f'(x) = \frac1{a^2} \lim_{h\to0}{(x+h)^2-x^2}h \\\\ f'(x) = \frac1{a^2} \lim_{h\to0}{(x^2+2xh+h^2)-x^2}h \\\\ f'(x) = \frac1{a^2} \lim_{h\to0}{2xh+h^2}h \\\\ f'(x) = \frac1{a^2} \lim_{h\to0}(2x+h) = \boxed{\frac{2x}{a^2}}$