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How do you find the derivative of #y=1/x^2#?

Answer 1

Christopher Allers

#dy /dx = -2/x^3 #

The derivative of # y = ax^n #

is #dy/dx = nax^(n-1) #

By rewriting # y = 1/x^2 # as #y = x^(-2) #

then it is in the form # ax^n #

#rArrdy/dx = - 2x^(-3) = - 2/(x^3) #

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Answer 2

Emily Ammerman

To find the derivative of ( y = \frac{1}{x^2} ), you can use the power rule for differentiation. The power rule states that if ( f(x) = x^n ), then ( f'(x) = nx^{n-1} ). Applying this rule to ( y = \frac{1}{x^2} ), we get:

[ \frac{dy}{dx} = -2x^{-3} ]

So, the derivative of ( y = \frac{1}{x^2} ) with respect to ( x ) is ( \frac{dy}{dx} = -\frac{2}{x^3} ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.