How do you differentiate #f(x)=x/(x-1)^2+x^2-4/(1-2x)# using the sum rule?

Answer 1

#f'(x)=-(x+1)/(x-1)^3+2x -8/(1-2x)^2 #

#f(x)=x/(x-1)^2+x^2-4(1-2x)^-1#
Use Quotients Rule: #f'(x)=(gf'-fg')/g^2# to find the derivative of the first part #x/(x-1)^2#
#f'(x)=((x-1)^2-x(2(x-1)))/(x-1)^4 +2x +4/(1-2x)^2 xx-2#
#f'(x)=((x-1)[x-1-2x])/(x-1)^4 +2x +4/(1-2x)^2 xx-2#
#f'(x)=-(x+1)/(x-1)^3+2x -8/(1-2x)^2 #
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Answer 2

To differentiate ( f(x) = \frac{x}{(x-1)^2} + \frac{x^2 - 4}{1-2x} ) using the sum rule, you differentiate each term separately and then add them together. The sum rule states that the derivative of the sum of two functions is the sum of the derivatives of those functions.

The derivative of ( \frac{x}{(x-1)^2} ) is obtained using the quotient rule, and the derivative of ( \frac{x^2 - 4}{1-2x} ) is obtained using the quotient rule as well.

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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.

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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