`(dy)/(dx)` ज्ञात कीजिए जब
(i) `y=sqrt(x)` (ii) `y=x^(5)+x^(4)+7` (iii) `y=x^(2)+4x^(-1//2)-3x^(-2)`

Explanation

(i) `y=xsqrt(x)implies(dy)/(dx)=d/(dx)(sqrt(x))=d/(dx)(x^(1//2))=1/2x^(1//2-1)=1/2x^(-1//2)=1/(1sqrt(x))`
(ii) `y=x^(5)+x^(4)+7implies(dy)/(dx)=d/(dx)(x^(5)+x^(4)+7)=d/(dx)(x^(5))+d/(dx)(x^(4))+d/(dx)(7)`
`=5x^(4)+4x^(3)=0+5x^(4)+4x^(3)`
(iii) `y=x^(2)+4x^(-1//2)-3x^(-2)implies(dy)/(dx)=d/(dx)(x^(2)+4x^(-1//2)-3x^(-2))=d/(dx)(x^(2))+d/(dx)(4x^(-1//2))-d/(dx)(3x^(-2))`
`=d/(dx)(x^(2))+4d/(dx)(x(-1//2))-3d/(dx)(x^(-2))=2x+4(-1/2)x^(-3//2)-3(-2)x^(-3)`
`=2x-2x^(-3//2)+6x^(-3)`