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How do you differentiate #(1+ (1/x))^3#?

Answer 1

Ezekiel Alexander

Derivative is #3(x+1/x)^2(1-1/x^2)#

We use the concept of function of a function. Let #f(x)=(g(x))^3#, where #g(x)=1+1/x# and then #f(x)=(1+1/x)^3#

Now according to chain formula #(df)/(dx)=(df)/(dg)*(dg)/(dx)#

As #f(x)=(g(x))^3#, #(df)/(dg)=3(g(x))^2#

and as #g(x)=x+1/x#, we have #(dg)/(dx)=1-1/x^2#

Hence #(df)/(dx)=3(g(x))^2*(dg)/(dx)=3(x+1/x)^2(1-1/x^2)#

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Answer 2

Evelyn Agard

To differentiate the expression (1 + (1/x))^3, you can use the chain rule. The derivative is -3(1 + (1/x))^2 * (1/x^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.