Ex 5.7, 6 - Find second order derivatives of ex sin 5x - Finding second order derivatives - Normal form

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  1. Chapter 5 Class 12 Continuity and Differentiability
  2. Serial order wise

Transcript

Ex 5.7, 6 Find the second order derivatives of the function ^ sin 5 Let y = ^ sin 5 Differentiating . . . . / = ( ( ^ " " sin 5 ))/ / = ( ^ )/ .sin 5 + ( ( sin 5 ))/ . ^ / = ^ .sin 5 + cos 5 ( (5 ))/ . ^ / = ^ . sin 5 + 5. ^ . cos 5 Again Differentiating . . . / ( / )= ( ( ^ . sin 5 " + " 5. ^ ." " cos 5 ))/ ( ^2 )/( ^2 ) = ( ( ^ . sin 5 ))/ + ( (5. ^ ." " cos 5 ))/ ( ^2 )/( ^2 ) = ( ( ^ sin 5 ))/ + 5 ( ( ^ ." " cos 5 ))/ ( ^2 )/( ^2 ) = (( ( ^ ))/ .sin 5 +( (sin 5 ))/ . ^ ) + 5 (( ( ^ ))/ .cos 5 +( (cos 5 ))/ . ^ ) ( ^2 )/( ^2 ) = ( ^ .sin 5 +(cos 5 ) .( ( 5 ))/ . ^ ) + 5 ( ^ .cos 5 +( sin 5 ) .( ( 5 ))/ . ^ ) ( ^2 )/( ^2 ) = ( ^ sin 5 +cos 5 .5. ^ ) + 5 ( ^ cos 5 sin 5 .5. ^ ) ( ^2 )/( ^2 ) = ^ sin 5 +5 ^ cos 5 +5 ^ cos 5 25 ^ sin 5 ( ^2 )/( ^2 ) = 10 ^ cos 5 24 ^ sin 5 ( ^ )/( ^ ) = 2 ^ ( 1 )

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