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

Answer 1

Scarlett Allison

The derivative is a linear operator, so you can differentiate term by term using the general formula:

#(d(x^n))/dx =n x^(n-1)#

#(df)/dx =d(x^2-3x-3x^(-2))/dx=d(x^2)/dx-3d(x)/dx-3d(x^-2)/dx =#

# = 2x -3 +6x^(-3)#

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Answer 2

Emma Aldridge

To find the derivative of ( f(x) = x^2 - 3x - 3x^{-2} ), you can use the power rule for differentiation:

For the term ( x^2 ), the derivative is ( 2x ).
For the term ( -3x ), the derivative is ( -3 ).
For the term ( -3x^{-2} ), the derivative is ( 6x^{-3} ) after applying the power rule.

Therefore, the derivative of ( f(x) ) is ( f'(x) = 2x - 3 + 6x^{-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.