Question

find derivativeof function of 1\√x​

Answer 1

Let f(x)=1√x , then y=1uandu=x12 , since √x=x12 . This means we have to differentiate both functions and multiply them. Let's start with y . By the power rule y'=1×u0=1 .

Answer 2

This function can be written as a composition of two functions, therefore we use the chain rule.

Explanation:

Let f(x)=√x , then y=1andu=x1/2 ,

since √x=x1/2 .

Simplifying further, we have that

y=uand=x−1/2

The chain rule states dy/dx=dy/du×du/dx

This means we have to differentiate both functions and multiply them. Let's start with

y .

By the power rule y'=1×u0=1 .

Now for u :Once again by the power rule we get:

Once again by the power rule we get:

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Hopefully this helps