# How do you use the power rule to differentiate #f(x)=1-x^2+3x^3sqrtx#?

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To use the power rule to differentiate (f(x) = 1 - x^2 + 3x^3\sqrt{x}), follow these steps:

- Differentiate each term of the function separately.
- For (1), the derivative is (0) since it's a constant.
- For (-x^2), apply the power rule: (d/dx(-x^2) = -2x).
- For (3x^3\sqrt{x}), apply the power rule: (d/dx(3x^3\sqrt{x}) = 9x^2\sqrt{x} + \frac{3}{2}x^3 \cdot \frac{1}{\sqrt{x}}).
- Simplify the derivative: (f'(x) = -2x + 9x^2\sqrt{x} + \frac{3}{2}x^{3/2}).

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