EXAMPLES OF DIFFERENTIAL COEFFICIENTS. 



1 



_i "/ i 



dx i 



dy . _. 

 =~ = sin 



40. y = xsm x. -~ = sm 



UX <y i i 



dy tan a; 



41. v = tan # tan l x. -/- = sec x tan \ 



I O\^V> */ UCtiJUL 1,0 "1 Q . 



aa; 1 +ar 



/ \n ^V / \-i / 



42. y = sin nx (sin a;) . -f- = n (sm#) sin (n+l}x. 



dx 



(sin nx) m dy mn (sin nx} 1 "' 1 cos (wa; wa?) 



43. y=-7 TT. -/ = a r^^ ^ 



(cos ma;) aa; (cos ma;) 



n+1 



44. y e~ atxt cos rx. - = e~ aS|r * (2a 2 a; cos ra; + r sin ra;) . 



j ^ 3!/ ^^ S1U fly 

 40. 7/ = -7-5 r^ . 



(sma;) 



sin a; -) 1 j-, 5T>- 3 (a; sin" 1 a;) cos x 



(sin a;) 4 



i n i * i du do 



45. v = log { } . -/- = . 



/v I fi y AVI /yt 



tl/U/ o Q**' 79 B**' 



a cos - 6 sm - 



A7 * ^ 



. \ dy x" (1 log x) 



48. ?/ = x . , = 5 



^ fji-** *T 



U'^' 



49. T/ = a^ in ~ 1;c . -p = 



dx 



x 



rJti _ 

 50. ?/ = e^. 



51. 3^ = 6^. 



