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Home / Doubts and Solutions/ICSE/Class 12 Science/Mathematics

Differentiate wrt x 

1)   (1+ cos x) / x 

2)   sin(2x)cos^2 (x)

Asked by nishabr7 8th July 2021, 11:19 PM
Answered by Expert
Answer:
Differentiation of  ( 1 + cosx ) / x
 
Let   u = (1+cosx)   and v = x
 
Hence differentiation of  u/v is given as 
 
begin mathsize 14px style fraction numerator d over denominator d x end fraction open parentheses u over v close parentheses space equals space fraction numerator v space begin display style fraction numerator d u over denominator d x end fraction end style minus u begin display style fraction numerator d v over denominator d x end fraction end style over denominator v squared end fraction end style
du/dx = -sinx   ,  dv/dx = 1 
 
begin mathsize 14px style fraction numerator d over denominator d x end fraction open parentheses fraction numerator 1 plus cos x over denominator x end fraction close parentheses space equals space minus space sin x space minus left parenthesis 1 plus cos x right parenthesis space end style
--------------------------------------------------------------
 
Differentiation of sin(2x) cos2x 
 
Let u = sin(2x) and v = cos2x 
 
begin mathsize 14px style fraction numerator d over denominator d x end fraction open parentheses u space v close parentheses space equals space u space fraction numerator d v over denominator d x end fraction space plus space v space fraction numerator d u over denominator d x end fraction end style
 
du/dx = 2 cos(2x)  ,  dv/dx = -2 cosx sinx = - sin2x
 
begin mathsize 14px style fraction numerator d over denominator d x end fraction open parentheses space sin left parenthesis 2 x right parenthesis space cos squared x space close parentheses space equals space minus space space sin squared 2 x space plus space 2 space cos squared x space cos left parenthesis 2 x right parenthesis space end style
 
Answered by Expert 18th September 2021, 10:04 AM
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