How do you find the derivative of y = 1/sqrt(x)

We have to find the derivative of 1/√x

Solution

We can express 1/√x as x-1/2

We know that

\(\frac{\mathrm{d} }{\mathrm{d} x}x^{n}=nx^{n-1}\)

Using the above equation we can solve 1/√x

=\(\frac{-1}{2}x^{-\frac{1}{2}-1}\)

=\(\frac{-1}{2}x^-\frac{3}{2}\)

=\(-\frac{1}{2x^{\frac{3}{2}}}\)

Answer

1/√x=\(-\frac{1}{2x^{\frac{3}{2}}}\)

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