Find the derivative of 1/√x

Let us assume f(x) = 1/√x

y = 1/u and and u = x1/2 since √x=x1/2

On simplification we get y =u and u = x-1/2

According to chain rule

\(\frac{dy}{dx}=\frac{dy}{du} X\frac{du}{dx}\)

So we have to differentiate both functions and multiply them.

By the power rule y’=1 ×u0=1

Again by using power rule we get

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

u’=\(-\frac{1}{2}. x^{-\frac{3}{2}}\)

u’=\(-\frac{1}{2\sqrt{x^{3}}}\)

f'(x)= y’ X u’

f'(x)= 1 X \(-\frac{1}{2\sqrt{x^{3}}}\)

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

Answer

Derivative of 1/√x= \(-\frac{1}{2\sqrt{x^{3}}}\)

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