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