x के सापेक्ष निम्नलिखित का अवकलन कीजिए :
(1) ` sqrt(3x +2 )+ 1/sqrt(2x^(2) +4)` (ii) ` e^(sec ^(2)x ) + 3 cos ^(1) x `
(iii) `log _(7) (log x)`

Explanation

(i) माना ` y = sqrt( 3x+2) +1/(sqrt(2x^(2)+4))`
` = ( 3x+ 2)^(1/2) + ( 2x^(2) +4)^(1/2)`
` (dy)/(dx) = 1/2 (3x + 2) ^(1/2) xxd/(dx) ( 3x+2) - 1/2(2x^(2)+4)^(-3/2) d/(dx) ( 2x^(2) +4)`
` 3/(2sqrt(3x+2))- 1/2 xx 4x xx 1/(2x^(2) + 4)^(3/2)`
` 3/(2sqrt(3x+2))- 1/2 xx 4x xx 1/(2x^(2) + 4)^3//2`
(ii) माना ` y = e^(sec^(2) x) + 3 cos ^(-1) x`
` :. (dy)/(dx) = e^(sec^(2)x ) * d/(dx) sec^(2) *x+3 (-1/(sqrt(1-x^(2))))`
` = e^(sec^(3)) x * 2 sec x d/(dx) sec * x+3 -1/ sqrt(1-x^(2) )`
` = 2 sec ^(2) x . tan x.e ^(sec^(2)x) - 3/(sqrt(1-x^(2)))`
(iii) माना ` y = log_(7) (log x) `
आधार परिवर्तन के सूत्रानुसार
` y = (log (logx))/(log7) `
` :. (dy)/(dx) = 1/(log7) d/(dx) log(logx) = 1/(log7) * 1/(log )* d/(dx) log x `
` = 1/(log7) * 1/log x *1/x = 1/(x log 7 log x )*`