Question

Derivative of 1/radical x

Answer 1

The derivative of
`\( (1)/(√(x)) \)` with respect to
`\( x \)` is
`\( -(1)/(2√(x^3)) \)`.

How did we get the value?

To find the derivative of
`\( (1)/(√(x)) \)` , you can use the rules of differentiation.

Let \( y =
`(1)/(√(x)) \)`. To find
`\( (dy)/(dx) \)`:

`\[ y = x^(-1/2) \]`

Now, apply the power rule for differentiation, which states that if
`\( y = x^n \)`, then
`\( (dy)/(dx) = nx^(n-1) \)`:

`\[ (dy)/(dx) = -(1)/(2)x^(-3/2) \]`

Now, you can simplify the expression:

`\[ (dy)/(dx) = -(1)/(2√(x^3)) \]`

So, the derivative of
`\( (1)/(√(x)) \)` with respect to
`\( x \)` is
`\( -(1)/(2√(x^3)) \)`.