Browse: Home   /   Product and Quotient rule   /   Assignments   /   Solution assignment 28 Product and Quotient rule

Solution assignment 28 Product and Quotient rule

Return to Assignments Product and Quotient rule

Assignment 28

Differentiate:

y=\displaystyle\frac{\ln(x)}{\sqrt{x}}

Solution

Here we can apply the quotient rule straigtforward:

f'(x)=\displaystyle\frac{1}{x}

g'(x)=[x^{-\frac{1}{2}}]'=-\displaystyle\frac{1}{2}x^{-\frac{3}{2}}

and thus:

y' = \displaystyle\frac{{\sqrt x\cdot\frac{1}{x} - \ln (x)\cdot - \frac{1}{2}x^{ - \frac{3}{2}} }}{{(\sqrt x )^2 }} = \displaystyle\frac{{x + \frac{1}{2}\ln (x)}}{{x^2 \sqrt x }}

Return to Assignments Product and Quotient rule

0
Web Design BangladeshWeb Design BangladeshMymensingh