# What is the derivative of #3*(sqrt x) - (sqrtx^3)#?

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The derivative of (3\sqrt{x} - \sqrt{x^3}) is (\frac{3}{2\sqrt{x}} - \frac{3x}{2\sqrt{x^3}}).

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The derivative of (3\sqrt{x} - \sqrt{x^3}) with respect to (x) is:

[ \frac{d}{dx} \left( 3\sqrt{x} - \sqrt{x^3} \right) = \frac{3}{2\sqrt{x}} - \frac{3x^{3/2}}{2\sqrt{x}} ]

Simplifying:

[ \frac{d}{dx} \left( 3\sqrt{x} - \sqrt{x^3} \right) = \frac{3}{2\sqrt{x}} - \frac{3x}{2\sqrt{x}} = \frac{3 - 3x}{2\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.

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