x के सापेक्ष निम्नलिखित का अवकलन कीजिए ।
(i) `e^(-x)` (ii) `sin (log x), x gt 0`
(iii) ` cos^(-1) (e^(x))` (iv) ` e ^(cos x)`

Explanation

(i) माना ` y = e^(-x)`
`dy/dx = d/dx e^(-x)`
` = e^(-x) d/dx ( -x) `
` = e^(-x) d/dx (-x)`
` = e^(-x) .`
(ii) माना ` y = sin ( log x) `
` dy/dx = d/dx sin ( log x) `
` = cos ( log x ) xx 1/x`
` = (cos (log x))/x `
(iii) माना ` y = cos^(-1) (e^(x)) `
` : . dy/dx = d/dy cos^(-1) (e^(x))`
` (-1)/ (sqrt(1- (e^(x))^(2))). d/ dx e^(x) `
(iv) माना ` y = e^(cos x) `
` dy/ dx = d/ dx e^(cos x) `
` -(sin x) . e^(cos x) `