How do you find #(dy)/(dx)# given #y^2=4x#?
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Now we will convert it into a differential equation
When we integrate (take the antiderivative) both the sides we get
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To find (dy)/(dx) given (y^2 = 4x), differentiate both sides of the equation with respect to (x).
[\frac{d}{dx}(y^2) = \frac{d}{dx}(4x)]
Using the chain rule and power rule, we get:
[2y\frac{dy}{dx} = 4]
Solve for (\frac{dy}{dx}):
[\frac{dy}{dx} = \frac{4}{2y} = \frac{2}{y}]
Substitute (y^2 = 4x) to get:
[\frac{dy}{dx} = \frac{2}{\sqrt{4x}} = \frac{1}{\sqrt{x}}]
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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.
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.
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.
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.
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