How do you differentiate #f(x) = 1 + 1/x + 7/x^2 + 1/x^3#?

Answer 1

Christopher Allers

Have a look:

You can write your function, using the Rule of Exponents, as: #f(x)=1+x^-1+7x^-2+x^-3#

and differentiate as #x^n# which gives you #nx^(n-1)#, to get:

#(df)/dx=0-x^-2-14x^-3-3x^-4=-1/x^2-14/x^3-3/x^4#

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Answer 2

Emma Aldridge

To differentiate the function f(x) = 1 + 1/x + 7/x^2 + 1/x^3, you can apply the power rule and the constant rule. The derivative of the function is f'(x) = -1/x^2 - 14/x^3 - 3/x^4.

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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.

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