Question

Find the answer and solve it








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Answer 1

Answer:

The answer is $-\frac{1}{4}x^{-\frac{3}{2}}+\frac{3}{4}x^{-\frac{5}{2}}$

Step-by-step explanation:

Given function is

            $y=\sqrt x+\frac{1}{\sqrt x}=x^{\frac{1}{2}}+x^{-\frac{1}{2}}$

     $\Rightarrow \frac{dy}{dx}=\frac{1}{2}x^{\frac{1}{2}-1}-\frac{1}{2}x^{-\frac{1}{2}-1}$, since $\frac{d}{dx}(x^n)=nx^{n-1}$

               $=\frac{1}{2}x^{-\frac{1}{2}}-\frac{1}{2}x^{-\frac{3}{2}$

Differentiate  again

     $\Rightarrow \frac{d^2y}{dx^2}=(\frac{1}{2})(-\frac{1}{2})x^{-\frac{3}{2}}-(\frac{1}{2})(-\frac{3}{2})x^{-\frac{5}{2}}$

               $=-\frac{1}{4}x^{-\frac{3}{2}}+\frac{3}{4}x^{-\frac{5}{2}}$