How do you find the derivative of #y=pi/(3x)^2#?

Answer 1

Charles Arocha

#(dy)/(dx) =-(2pi)/(9x^3)#

#y=pi/((3x)^2) = pi/9x^(-2)#

#(dy)/(dx) = pi/9(-2x^(-3)) =-(2pi)/(9x^3)#

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Answer 2

Emma Aldridge

To find the derivative of (y = \frac{\pi}{(3x)^2}), you can use the power rule for differentiation. The power rule states that if you have a function of the form (f(x) = ax^n), then its derivative (f'(x)) is given by (f'(x) = anx^{n-1}). Applying this rule to (y = \frac{\pi}{(3x)^2}), we get:

[y' = \frac{d}{dx} \left( \frac{\pi}{(3x)^2} \right) = \frac{d}{dx} \left( \pi \cdot (3x)^{-2} \right)]

[= -2\pi \cdot (3x)^{-2-1} = -2\pi \cdot 3^{-2} \cdot x^{-2-1} = -\frac{2\pi}{9x^3}]

So, the derivative of (y = \frac{\pi}{(3x)^2}) is (y' = -\frac{2\pi}{9x^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.