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How do you differentiate #x^-7 - 7x^-1#?

Answer 1

Emma Aldridge

#-7x^-8+7x^-2#

Let #y=x^-7-7x^-1#

#y'=(x^-7)'-(7x^-1)'#

By the power rule #(x^n)'=nx^(n-1)# we get:

#y'=-7x^(-7-1)-7times(-1x^(-1-1))#

By simplifying, we get:

#-7x^-8+7x^-2#

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Answer 2

Samantha Adkison

To differentiate ( x^{-7} - 7x^{-1} ), you apply the power rule for differentiation, which states that the derivative of ( x^n ) with respect to ( x ) is ( nx^{n-1} ).

So, the derivative of ( x^{-7} ) with respect to ( x ) is ( -7x^{-8} ), and the derivative of ( 7x^{-1} ) with respect to ( x ) is ( -7x^{-2} ).

Therefore, the differentiation of ( x^{-7} - 7x^{-1} ) with respect to ( x ) is ( -7x^{-8} - (-7x^{-2}) ), which simplifies to ( -7x^{-8} + 7x^{-2} ).

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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.