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NEET Class neet Answered

I understood the sum please give me a detailed step-by-step explain action of how there differentiated F to get the ans
question image
Asked by rheavirginkar | 14 Apr, 2019, 07:22: PM
answered-by-expert Expert Answer
The differentiation rule to be applied in this question is as follows

begin mathsize 12px style I f space space y left parenthesis x right parenthesis space equals space fraction numerator u left parenthesis x right parenthesis over denominator v left parenthesis x right parenthesis end fraction space comma space space t h e n space fraction numerator d y over denominator d x end fraction equals space fraction numerator v begin display style fraction numerator d u over denominator d x end fraction end style space minus space u space begin display style fraction numerator d v over denominator d x end fraction end style over denominator v squared end fraction end style
Hence differentiation is done as follows
 
begin mathsize 12px style F space equals space K space Q squared space fraction numerator space d over denominator open parentheses d squared plus begin display style R squared over 4 end style close parentheses to the power of begin display style bevelled 3 over 2 end style end exponent end fraction space space
fraction numerator d F over denominator d d end fraction space equals space K space Q squared space fraction numerator open parentheses d squared plus R squared over 4 close parentheses to the power of bevelled 3 over 2 end exponent space minus space d open parentheses begin display style 3 over 2 end style close parentheses open parentheses d squared plus R squared over 4 close parentheses to the power of bevelled 1 half end exponent 2 d over denominator open parentheses d squared plus begin display style R squared over 4 end style close parentheses cubed end fraction space equals space K Q squared space open parentheses d squared plus R squared over 4 close parentheses to the power of bevelled 1 half end exponent over open parentheses d squared plus R squared over 4 close parentheses cubed space cross times open parentheses d squared plus R squared over 4 space minus space 3 d squared close parentheses space.......... left parenthesis 1 right parenthesis
T o space g e t space m a x i m u m space F comma space w e space p u t space fraction numerator d F over denominator d d end fraction space equals space 0 space. space space H e n c e space f r o m space e q n. left parenthesis 1 right parenthesis comma space w e space g e t space space open parentheses R squared over 4 space minus space 2 d squared close parentheses space equals space 0
h e n c e space comma space space space d squared space equals space R squared over 8 space space o r space space space space d space equals space fraction numerator R over denominator 2 square root of 2 end fraction end style
Answered by Thiyagarajan K | 14 Apr, 2019, 08:21: PM
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