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How do you differentiate #f(x)=sqrt((1-x)/(1+x))#?

Answer 1

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

#f(x)=sqrt(1-x)/sqrt(1+x)# By applying quotient rule, Let #u=sqrt(1-x)# and #v=sqrt(1+x)# #f'(x)=(u'v-v'u)//v^2# #f'(x)={1/2root(-1/2)(1-x)*sqrt(1+x)-1/2root(-1/2)(1+x)*sqrt(1-x)}/(1+x)# #f'(x)=1/2{(sqrt(1+x)/sqrt(1-x))-(sqrt(1-x)/sqrt(1+x)}//(1+x)# #f'(x)=1/2{1+x-1+x}/((1+x)sqrt(1-x^2))# #f'(x)=x/((1+x)sqrt(1-x^2))#

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Answer 2

Christopher Agresta

To differentiate (f(x) = \sqrt{\frac{1-x}{1+x}}), you can use the chain rule. The chain rule states that if you have a function within a function, you differentiate the outer function first and then the inner function, multiplying the results together.

Here's how to differentiate (f(x)):

Let (u = \frac{1-x}{1+x}).
Rewrite (f(x)) as (f(x) = \sqrt{u}).
Differentiate (f(x)) with respect to (u) first: (\frac{d}{du}\sqrt{u}).
Then differentiate (u) with respect to (x): (\frac{d}{dx}\left(\frac{1-x}{1+x}\right)).
Multiply the results of steps 3 and 4 together to find the derivative of (f(x)).

Applying the chain rule, you can compute the derivative of (f(x)).

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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.