# How do you find the derivative of the function #f(x)=-2x^-3+x^2-7#?

# 6x^-4 + 2x #

applying the 'power rule'

Next, each term in the function receives this application.

(A constant term's derivative is 0 )

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To find the derivative of the function (f(x) = -2x^{-3} + x^2 - 7), you can use the power rule and the constant rule of differentiation. The derivative of a constant is zero, and for a term of the form (ax^n), the derivative is (anx^{n-1}). Applying these rules:

(f'(x) = \frac{d}{dx}(-2x^{-3}) + \frac{d}{dx}(x^2) + \frac{d}{dx}(-7))

(f'(x) = -2 \cdot (-3)x^{-4} + 2x^{2-1} + 0)

(f'(x) = 6x^{-4} + 2x)

Simplify the expression:

(f'(x) = \frac{6}{x^4} + 2x)

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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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